advances in multi domain lattice boltzmann grid refinement grid refinement has been addressed by different authors in the lattice boltzmann method community the information communication and reconstruction on grid transitions is of crucial importance from the accuracy and numerical stability point of view while a decimation is performed when going from the fine to the coarse grid a reconstruction must performed to pass form the coarse to the fine grid in this context we introduce a decimation technique for the copy from the fine to the coarse grid based on a filtering operation we show this operation to be extremely important because a simple copy of the information is not sufficient to guarantee the stability of the numerical scheme at high reynolds numbers then we demonstrate that to reconstruct the information a local cubic interpolation scheme is mandatory in order to get a precision compatible with the order of accuracy of the lattice boltzmann method these two fundamental extra steps are validated on two classical 2d benchmarks the 2d circular cylinder and the 2d dipole wall collision the latter is especially challenging from the numerical point of view since we allow strong gradients to cross the refinement interfaces at a relatively high reynolds number of 5000 a very good agreement is found between the single grid and the refined grid cases the proposed grid refinement strategy has been implemented in the parallel open source library palabos

a method for improved distribution concentration in the time frequency analysis of multicomponent signals using the l wigner distribution the energy location in the cohen class of time frequency distributions is analyzed if the instantaneous frequency is linear then only the wigner distribution produces the ideal energy concentration the scaled version of the wigner distribution l wigner distribution is used to improve the time frequency representation of signals with nonlinear instantaneous frequencies in the case of multicomponent signals the cross terms appearing in the wigner distribution and in the l wigner distribution can be easily removed or reduced in a computationally very efficient way the theory is illustrated on the numerical examples with multicomponent noisy signals

acceleration of steady state lattice boltzmann simulations for exterior flows the simulation of a stationary fluid flow past an obstacle by the lattice boltzmann method lbm in two dimensions is discussed the combination of second order expressions for far field boundary conditions and a suitable treatment of the no slip boundary condition at the obstacle surface with the nested grid refinement technique can be applied to the lbm resulting in a highly efficient method for the treatment of exterior flows furthermore via replacing the nested time stepping by local time stepping the resolution process can be substantially accelerated a highly accurate drag coefficient was used to make an error assessment for various no slip boundary conditions imposed on the obstacle surface the analysis showed that the equilibrium method for treating the no slip conditions is superior to halfway bounce back and full way bounce back no slip conditions when the relaxation time ensuremath tau 1 also a ensuremath tau dependence test was made to evaluate the performance of different methods in the treatment of the no slip boundary conditions

proteus a coupled iterative force correction immersed boundary cascaded lattice boltzmann solver for moving and deformable boundary applications abstract many realistic fluid flow problems are characterised by high reynolds numbers and complex moving or deformable geometries in our previous study we presented a novel coupling between an iterative force correction immersed boundary and a multi domain cascaded lattice boltzmann method falagkaris et al and investigated flows around rigid bodies at reynolds numbers up to 1 0 5 here we extend its application to flows around moving and deformable bodies with prescribed motions emphasis is given on the influence of the internal mass on the computation of the aerodynamic forces including deforming boundary applications where the rigid body approximation is no longer valid both the rigid body and the internal lagrangian points approximations are examined the resulting solver has been applied to viscous flows around an in line oscillating cylinder a pitching foil a plunging sd7003 airfoil and a plunging and flapping naca 0014 airfoil good agreement with experimental results and other numerical schemes has been obtained it is shown that the internal lagrangian points approximation accurately captures the internal mass effects in linear and angular motions as well as in deforming motions at reynolds numbers up to 4 1 0 4 in all cases the aerodynamic loads are significantly affected by the internal fluid forces

lattice boltzmann model for the incompressible navier stokes equation in this paper a lattice boltzmann lb model to simulate incompressible flow is developed the main idea is to explicitly eliminate the terms of o m2 where m is the mach number due to the density fluctuation in the existing lb models in the proposed incompressible lb model the pressure p instead of the mass density is the independent dynamic variable the incompressible navier stokes equations are derived from the incompressible lb model via chapman enskog procedure numerical results of simulations of the plane poiseuille flow driven either by pressure gradient or a fixed velocity profile at entrance as well as of the 2d womersley flow are presented the numerical results are found to be in excellent agreement with theory

introducing a modified exact difference method for incorporating unsteady and non uniform force terms in lattice kinetic models abstract the exact difference method edm of kupershtokh 2004 in this work is modified to accurately incorporate unsteady non uniform force terms into lattice kinetic models we use the characteristic scheme for integrating the boltzmann equation along with the trapezoidal rule to estimate the integration results the method is based on discretizing the total derivative of the equilibrium distribution function edf in the edm using a central second order scheme instead of a first order method it is shown that the assumption of constant density in calculating the total derivative of the edf is not necessary in the limit of incompressible fluid flows using the chapman enskog analysis it is shown that the present method can be applied to both the standard lattice boltzmann method and the recently introduced constant speed kinetic model cskm of zadehgol and ashrafizaadeh 2014 the following benchmark flows are simulated i womersley flow ii hartmann flow iii unsteady taylor green vortex flow and iv the circular interface using the cskm and the results are in excellent agreement with the analytical solutions

force evaluation in the lattice boltzmann method involving curved geometry the present work investigates two approaches for force evaluation in the lattice boltzmann equation the momentum exchange method and the stress integration method on the surface of a body the boundary condition for the particle distribution functions on curved geometries is handled with second order accuracy based on our recent works mei et al j comput phys 155 307 1999 ibid 161 680 2000 the stress integration method is computationally laborious for two dimensional flows and in general difficult to implement for three dimensional flows while the momentum exchange method is reliable accurate and easy to implement for both two dimensional and three dimensional flows several test cases are selected to evaluate the present methods including i two dimensional pressure driven channel flow ii two dimensional uniform flow past a column of cylinders iii two dimensional flow past a cylinder asymmetrically placed in a channel with vortex shedding iv three dimensional pressure driven flow in a circular pipe and v three dimensional flow past a sphere the drag evaluated by using the momentum exchange method agrees well with the exact or other published results

depth averaged lattice boltzmann and finite element methods for single phase flows in fractures with obstacles abstract we use lattice boltzmann method lbm mrt and cumulant schemes to study the performance and accuracy of single phase flow modeling for propped fractures the simulations are run using both the two and three dimensional stokes equations and a 2 5d stokes brinkman approximate model the lbm results are validated against finite element method fem simulations and an analytical solution to the stokes brinkman flow around an isolated circular obstacle both lbm and fem 2 5d stokes brinkman models are able to reproduce the analytical solution for an isolated circular obstacle in the case of 2d stokes and 2 5d stokes brinkman models the differences between the extrapolated fracture permeabilities obtained with lbm and fem simulations for fractures with multiple obstacles are below 1 the differences between the fracture permeabilities computed using 3d stokes lbm and fem simulations are below 8 the differences between the 3d stokes and 2 5 stokes brinkman results are less than 7 for fem study and 8 for the lbm case the velocity perturbations that are introduced around the obstacles are not fully captured by the parabolic velocity profile inherent to the 2 5d stokes brinkman model

a simplified finite volume lattice boltzmann method for simulations of fluid flows from laminar to turbulent regime part i numerical framework and its application to laminar flow simulation abstract in this paper an unstructured grid based finite volume lattice boltzmann method fvlbm that can be used for the simulation of incompressible laminar flows is presented and studied in detail this method is derived from a simple modification of the cell vertex unstructured grid based fvlbm proposed by stiebler et al 2006 compared with other complex flux reconstruction methods the present scheme has a low computational cost and can also achieve second order spatial accuracy furthermore depending on the use of the different temporal discretization schemes the temporal accuracy can be adjusted for both steady and unsteady flows besides some comparisons of the computational cost and accuracy with another fvlbm scheme are also presented meanwhile different boundary conditions are illustrated that are easy to implement on complex geometries to validate the present method four cases are carried out including a couette flow driven by one plate for an accuracy test flow in a square cavity flow around a single circular cylinder and a more complex flow around double circular cylinders numerical experiments show that the present scheme can simulate steady and unsteady flows at relatively high reynolds number with relatively few grid cells thus demonstrating the good capability of the present method

parametrization of the cumulant lattice boltzmann method for fourth order accurate diffusion part ii application to flow around a sphere at drag crisis the optimized cumulant lattice boltzmann method with fourth order accurate diffusion is used to simulate the flow around a sphere up to reynolds number 106 the drag crisis is well captured by the method we demonstrate with our results that the drag crisis corresponds to an almost discrete jump in the flow conditions the intermediate values of drag in a small range of reynolds numbers around the drag crisis observed in averaged data sets are found to originate from the flow switching between the high and the low drag conditions around the critical reynolds number the time spent in the low drag condition increases with the reynolds number such that the average drag curve has a finite steepness

method of simulating unsteady turbomachinery flows with multiple perturbations currently time marching methods for unsteady turbomachinery flow calculations suffer from the inability to deal with multiple perturbations in a single passage solution a new periodic boundary condition method has been proposed in which one can perform a single passage solution with multiple perturbations at the periodic boundaries all of the perturbations are identified by their own phase shifted periodicities and approximated by fourier series a combined parameter is chosen for the fourier transform so that the fourier coefficients can be efficiently updated corrections on both the variables at a current time level and on the fourier coefficients are carried out repeatedly until a periodic state is reached numerical examples for oscillating cascade flows subject to inlet outlet perturbations have demonstrated the validity of the present method and its ability to deal with situations of practical interest

acceleration of lattice bgk schemes with grid refinement abstract the lbgk method with local grid refinement has been shown to be an efficient and accurate tool for the simulation of incompressible viscous flows over complex geometries in the present study further improvement of this concept is proposed enabling the use of smaller amount of time steps on refined grids without impairing the spatial or temporal accuracy this extension of the lbgk method has been proved by analytical and numerical investigations the gain in computational time was found to be significant

asymptotic analysis of lattice boltzmann boundary conditions in this article we use a general method for the analysis of finite difference schemes to investigate lattice boltzmann algorithms for navier stokes problems with dirichlet boundary conditions several link based boundary conditions for commonly used lattice boltzmann bgk models are considered with our method the accuracy of the algorithms can be exactly predicted moreover the analytical results can be used to construct new algorithms which is demonstrated with a corrected bounce back rule that requires only local evaluations but still yields second order accuracy for the velocity the analysis is applicable to general geometries and instationary flows

some progress in lattice boltzmann method part i nonuniform mesh grids a new lattice boltzmann algorithm is proposed to simulate the navier stokes equation on arbitrary nonuniform mesh grids the new algorithm retains the advantages of the lattice boltzmann method parallel of algorithm ease of programming and ability to incorporate microscopic interactions a simulation of flow in a two dimensional symmetric channel with sudden expansion is carried out using the new algorithm on a nonuniform mesh the results of the simulation are in excellent agreement with previous experimental and numerical results

a mass conserving boundary condition for the lattice boltzmann equation method in lattice boltzmann lb simulations the widely used wall boundary conditions bcs proposed by filipova and hanel fh and mei luo and shyy mls result in constant mass leakage in certain circumstances in this paper we have analyzed the source of the leakage based on this analysis we propose a second order accurate mass conserving wall bc in our bc the distribution function at a wall node is decomposed into its equilibrium and non equilibrium parts the mass conservation is guaranteed by enforcing a mass conserving rule in the construction of the fictitious equilibrium distribution part we have shown through several benchmark test problems involving steady and unsteady flows that our new bc not only eliminates the constant mass leakage but also has many other advantages over the fh and mls bcs

central moment lattice boltzmann schemes with fixed and moving immersed boundaries lattice boltzmann lb schemes based on the relaxation of central moments have recently proved valuable in simulating flows with an improved stability with respect to the original single relaxation time bgk formulation while preserving the accuracy of the latter this has been assessed mainly for flows in simple geometries e g in periodic domains or with fixed rigid straight boundaries in the present study the properties of central moment lb schemes have been investigated against flow configurations involving arbitrarily shaped possibly moving boundaries within the framework of the so called immersed boundary ib method namely the presence of boundaries is accounted by an external force acting on the fluid that is encompassed in the central moment lb algorithm accuracy and stability issues are examined in comparison with existing results from the literature and lb simulations based on the original bgk scheme our results show that central moment lb schemes accompanied by the ib method provide an efficient tool for fluid structure interaction simulations

second order interpolation of the flow field in the lattice boltzmann method we propose a scheme to reconstruct the flow field up to second order in a cell composed of four lattices nodes in 2 dimensions the information contained in the higher order moments of the distribution functions is used to construct an interpolation scheme of second order for the velocity field

a filtered cumulant lattice boltzmann method for violent two phase flows abstract the lattice boltzmann method lbm has been successfully applied to simulate various two phase flow problems such as rayleigh taylor instability rising bubble and droplet dynamics however the method known as two phase lbm faces difficulty in simulating violent two phase flow problems such as dam breaking and liquid jet breakup where the density ratio and reynolds number are high and there are rapid and complex topological changes in this paper we address the problem by using a filtered cumulant lbm the incompressible two phase flow equations are solved by using a velocity based formulation of two phase lbm with a cumulant collision model to stably simulate problems with high density ratio and reynolds number there is no pressure iteration in this formulation and we can keep the simplicity of the cumulant model to further enhance the stability in violent flows a second order filter is applied on the velocity field which can be turned off for non violent flows for interface capturing a conservative phase field lbm which guarantees the mass conservation is employed the proposed method is first validated using five non violent flow problems and the results are in good agreements with experimental and computational references the proposed method is then employed to solve three violent flow problems and the results are in qualitatively good agreements with experimental and computational references the proposed method is more diffusive than the unfiltered model but is stable for all problems simulated in this paper these results can be used as a preliminary study on violent two phase flow simulation using two phase lbm

regular article an accurate curved boundary treatment in the lattice boltzmann method the lattice boltzmann equation lbe is an alternative kinetic method capable of solving hydrodynamics for various systems major advantages of the method are due to the fact that the solution for the particle distribution functions is explicit easy to implement and natural to parallelize because the method often uses uniform regular cartesian lattices in space curved boundaries are often approximated by a series of stairs that leads to reduction in computational accuracy in this work a second order accurate treatment of the boundary condition in the lbe method is developed for a curved boundary the proposed treatment of the curved boundaries is an improvement of a scheme due to o filippova and d hanel 1998 j comput phys 147 219 the proposed treatment for curved boundaries is tested against several flow problems 2 d channel flows with constant and oscillating pressure gradients for which analytic solutions are known flow due to an impulsively started wall lid driven square cavity flow and uniform flow over a column of circular cylinders the second order accuracy is observed with a solid boundary arbitrarily placed between lattice nodes the proposed boundary condition has well behaved stability characteristics when the relaxation time is close to 1 2 the zero limit of viscosity the improvement can make a substantial contribution toward simulating practical fluid flow problems using the lattice boltzmann method

equivalent partial differential equations of a lattice boltzmann scheme we show that when we formulate the lattice boltzmann equation with a small time step dt and an associated space scale dx a taylor expansion joined with the so called equivalent equation methodology leads to establishing macroscopic fluid equations as a formal limit we recover the euler equations of gas dynamics at the first order and the compressible navier stokes equations at the second order

linear stability and isotropy properties of athermal regularized lattice boltzmann methods the present work proposes a general methodology to study stability and isotropy properties of lattice boltzmann lb schemes as a first investigation such a methodology is applied to better understand these properties in the context of regularized approaches to this extent linear stability analyses of two dimensional models are proposed the standard bhatnagar gross krook collision model the original precollision regularization and the recursive regularized model where off equilibrium distributions are partially computed thanks to a recursive formula a systematic identification of the physical content carried by each lb mode is done by analyzing the eigenvectors of the linear systems stability results are then numerically confirmed by performing simulations of shear and acoustic waves this work allows drawing fair conclusions on the stability properties of each model in particular among the aforementioned models recursive regularization turns out to be the most stable one for the d2q9 lattice especially in the zero viscosity limit two major properties shared by every regularized model are highlighted 1 a mode filtering property and 2 an incorrect and broadly anisotropic dissipation rate of the modes carrying physical waves in under resolved conditions the first property is the main source of increased stability especially for the recursive regularization it is a direct consequence of the reconstruction of off equilibrium populations before each collision process decreasing the rank of the system of discrete equations the second property seems to be related to numerical errors directly induced by the equilibration of high order moments in such a case this property is likely to occur with any collision model that follows such a stabilization methodology

lattice boltzmann computational fluid dynamics in three dimensions the recent development of the lattice gas method and its extension to the lattice boltzmann method have provided new computational schemes for fluid dynamics both methods are fully paralleled and can easily model many different physical problems including flows with complicated boundary conditions in this paper basic principles of a lattice boltzmann computational method are described and applied to several three dimensional benchmark problems in most previous lattice gas and lattice boltzmann methods a face centered hyper cubic lattice in four dimensional space was used to obtain an isotropic stress tensor to conserve computer memory we develop a model which requires 14 moving directions instead of the usual 24 directions lattice boltzmann models describing two phase fluid flows and magnetohydrodynamics can be developed based on this simpler 14 directional lattice comparisons between three dimensional spectral code results and results using our method are given for simple periodic geometries an important property of the lattice boltzmann method is that simulations for flow in simple and complex geometries have the same speed and efficiency while all other methods including the spectral method are unable to model complicated geometries efficiently

multi block lattice boltzmann method extension to 3d and validation in turbulence abstract in this paper a multi block method is applied to 3d problems in this application interpolation schemes are carefully addressed to avoid the inconsistency when information is transferred from coarse to fine blocks two test cases are employed to assess information transfer scheme and accuracy improvement with respect to grid refinement

galilean invariance study on different lattice boltzmann fluid solid interface approaches for vortex induced vibrations abstract the present work compares fluid solid interface approaches for the lattice boltzmann method lbm to study vortex induced vibrations viv two classes of fluid solid interface approaches namely the partially saturated methods psm noble and torczynski 1998 holdych 2003 krause et al 2017 trunk et al 2018 and moving boundary methods mbm bouzidi et al 2001 lallemand and luo 2003 yu et al 2003 ginzburg et al 2008 and filippova and hanel 1998 mei et al 1999 2000 are investigated first the galilean invariance of aerodynamic coefficients obtained by each scheme is examined the bhatnagar gross krook bgk lbm is utilized to simulate an eccentrically positioned cylinder in a transient couette flow in addition various refill methods for mbm and volume approximation techniques for psm are tested besides different error norms and a grid independence study of each method the galilean invariance violating frequencies are studied as well these error calculations are used to choose a representative for each class to simulate vortex shedding the viv test case describes a transverse oscillation of a cylinder in a freestream at a reynolds number of 100 both free and forced cylinder oscillations are examined to study known phenomena as lock in and lock out zones the results of mbm and psm are in good agreement to literature values and prove the suitability for viv simulations

grid refinement in lattice boltzmann methods based on volumetric formulation abstract we describe a general algorithmic concept for grid refinement in the lattice boltzmann method unlike most of the previously known approaches the present one is based on volumetric formulation so that conservation laws are exactly guaranteed

on the application of the lattice boltzmann method to the investigation of glottal flow the production of voice is directly related to the vibration of the vocal folds which is generated by the interaction between the glottal flow and the tissue of the vocal folds in the current study the aerodynamics of the symmetric glottis is investigated numerically for a number of static configurations the numerical investigation is based on the lattice boltzmann method lbm which is an alternative approach within computational fluid dynamics compared to the traditional navier stokes computational fluid dynamics methods the lbm is relatively easy to implement and can deal with complex geometries without requiring a dedicated grid generator the multiple relaxation time model was used to improve the numerical stability the results obtained with lbm were compared to the results provided by a traditional navier stokes solver and experimental data it was shown that lbm results are satisfactory for all the investigated cases

on rotational invariance of lattice boltzmann schemes we propose the derivation of acoustic type isotropic partial differential equations that are equivalent to linear lattice boltzmann schemes with a density scalar field and a momentum vector field as conserved moments the corresponding linear equivalent partial differential equations are generated with a new berliner version of the taylor expansion method the details of the implementation are presented these ideas are applied for the d2q9 d2q13 d3q19 and d3q27 lattice boltzmann schemes some limitations associated with necessary stability conditions are also presented

lattice boltzmann model for free surface flow and its application to filling process in casting a generalized lattice boltzmann model to simulate free surface is constructed in both two and three dimensions the proposed model satisfies the interfacial boundary conditions accurately a distinctive feature of the model is that the collision processes is carried out only on the points occupied partially or fully by the fluid to maintain a sharp interfacial front the method includes an anti diffusion algorithm the unknown distribution functions at the interfacial region are constructed according to the first order chapman enskog analysis the interfacial boundary conditions are satisfied exactly by the coefficients in the chapman enskog expansion the distribution functions are naturally expressed in the local interfacial coordinates the macroscopic quantities al the interface are extracted from the least square solutions of a locally linearized system obtained from the known distribution functions the proposed method does not require any geometric front construction and is robust for any interfacial topology simulation results of realistic filling process are presented rectangular cavity in two dimensions and hammer box campbell box sheffield box and motorblock in three dimensions to enhance the stability at high reynolds numbers various upwind type schemes are developed free slip and no slip boundary conditions are also discussed

extensive analysis of the lattice boltzmann method on shifted stencils standard lattice boltzmann methods lbms are based on a symmetric discretization of the phase space which amounts to study the evolution of particle distribution functions pdfs in a reference frame at rest this choice induces a number of limitations when the simulated flow speed gets closer to the sound speed such as velocity dependent transport coefficients the latter issue is usually referred to as a galilean invariance defect to restore the galilean invariance of lbms it was proposed to study the evolution of pdfs in a comoving reference frame by relying on asymmetric shifted lattices n frapolli s s chikatamarla and i v karlin phys rev lett 117 010604 2016 from the numerical viewpoint this corresponds to overcoming the rather restrictive courant friedrichs lewy conditions on standard lbms and modeling compressible flows while keeping memory consumption and processing costs to a minimum therefore using the standard first neighbor stencils in the present work systematic physical error evaluations and stability analyses are conducted for different discrete equilibrium distribution functions edfs and collision models thanks to them it is possible to 1 better understand the effect of this solution on both physics and stability 2 assess its viability as a way to extend the validity range of lbms and 3 quantify the importance of the reference state as compared to other parameters such as the equilibrium state and equilibration path the results clearly show that in theory the concept of shifted lattices allows the scheme to deal with arbitrarily high values of the nondimensional velocity furthermore just like the zero mach flow for the standard stencils it is observed that setting the shift velocity to the fluid velocity results in optimal physical and numerical properties in addition a detailed analysis of the obtained results shows that the properties of different collision models and edfs remain unchanged under the shift of stencil in other words by introducing a velocity shift in the stencil the optimal operating point in terms of physics and numerics will also be shifted by the same vector regardless of the edf or collision model considered eventually while limited to the d2q9 stencil with the nine possible first neighbor shifts the present study and corresponding conclusions can be extended to other stencils and velocity shifts in a straightforward manner

generalized local equilibrium in the cascaded lattice boltzmann method by realizing the insufficient degree of galilean invariance of the traditional multiple relaxation time collision operators geier et al phys rev e 73 066705 2006 proposed to relax differently the moments shifted by the macroscopic velocity leading to the so called cascaded lattice boltzmann method lbm this paper points out that a the cascaded lbm essentially consists in adopting a generalized local equilibrium in the frame at rest b this new equilibrium does not affect the consistency of lbm and finally c if the raw moments are relaxed in the frame at rest as usual and the number of relaxation frequencies is reduced the proposed derivation leads to the two relaxation time collisional operator with proper polynomial equilibrium

second order boundary schemes for the lattice boltzmann method with general propagation abstract this paper is concerned with the boundary treatment of the lattice boltzmann method lbm with general propagation for the incompressible navier stokes equations since the propagation step involves three grid points constructing effective boundary schemes for such method is highly nontrivial to address this problem we first construct an auxiliary boundary scheme under the diffusive scaling by using the maxwell iteration based on this scheme and the interpolations of both distribution functions and fluid velocities we propose a parameterized boundary scheme for the lbm with general propagation the scheme thus obtained not only has second order accuracy under the diffusive scaling for curved boundaries but also possesses good stability several specific schemes are also provided and their accuracy and stability are verified via four flow problems with both straight and curved boundaries it should be noted that the proposed boundary scheme can also be used for the standard lbm

on the three dimensional central moment lattice boltzmann method a three dimensional 3d lattice boltzmann method based on central moments is derived two main elements are the local attractors in the collision term and the source terms representing the effect of external and or self consistent internal forces for suitable choices of the orthogonal moment basis for the three dimensional twenty seven velocity d3q27 and its subset fifteen velocity d3q15 lattice models attractors are expressed in terms of factorization of lower order moments as suggested in an earlier work the corresponding source terms are specified to correctly influence lower order hydrodynamic fields while avoiding aliasing effects for higher order moments these are achieved by successively matching the corresponding continuous and discrete central moments at various orders with the final expressions written in terms of raw moments via a transformation based on the binomial theorem furthermore to alleviate the discrete effects with the source terms they are treated to be temporally semi implicit and second order with the implicitness subsequently removed by means of a transformation as a result the approach is frame invariant by construction and its emergent dynamics describing fully 3d fluid motion in the presence of force fields is galilean invariant numerical experiments for a set of benchmark problems demonstrate its accuracy

rotational invariance in the three dimensional lattice boltzmann method is dependent on the choice of lattice the lattice boltzmann method has recently gained popularity as a tool for simulating complex fluid flows it uses discrete sets of velocity vectors or lattices to create a reduced model of the molecular dynamics of a continuum fluid while several lattices are believed to behave isotropically there are reports of qualitatively incorrect results however thus far the reason as to why a lack of isotropy occurs is not known based on the hypothesis that lower order lattices may not display rotational invariance this study tests the isotropy of the d3q15 d3q19 and d3q27 lattices by performing simulations at intermediate reynolds numbers 50 500 and low knudsen number 250 the d3q15 and d3q19 lattices produced different results depending on the plane of the lattice with which the flow was aligned lattice planes with fewer than six velocity vectors consistently produced results which were qualitatively different from the planes with six or more velocity vectors these errors were not observed at re 50 or when a d3q27 lattice was used they appeared to be independent of grid density collision operator and ma this suggests that the lattices which contain these planes are not fully isotropic and therefore do not properly replicate the behavior of a real fluid in this particular situation notably downstream from the expansion predictions made using these models in more complex geometries may therefore be affected by the orientation of the lattice when using lbm in cfd simulation including validation this study highlights the need for caution to ensure that the solution obtained is independent of the lattice orientation throughout the domain

proteus a coupled iterative force correction immersed boundary multi domain cascaded lattice boltzmann solver abstract most realistic fluid flow problems are characterized by high reynolds numbers and complex boundaries over the last ten years immersed boundary methods that are able to cope with realistic geometries have been applied to lattice boltzmann lb methods these methods however have normally been applied to low reynolds number problems here we present a novel coupling between an iterative force correction immersed boundary zhang et al 2016 and a multi domain cascaded lb method the iterative force correction immersed boundary method has been selected due to the improved accuracy of the computation while the cascaded lb formulation is used due to its superior stability at high reynolds numbers the coupling is shown to improve both the stability and numerical accuracy of the solution the resulting solver has been applied to viscous flow up to a reynolds number of 100000 passed a naca 0012 airfoil at a 10 degree angle of attack good agreement with results obtained using a body fitted navier stokes solver has been obtained the formulation provides a straight forward and efficient method for modeling realistic geometries and could easily be extended to problems with moving boundaries

single node second order boundary schemes for the lattice boltzmann method abstract based on our recently developed maxwell iteration for the lattice boltzmann method we propose a class of single node boundary schemes for dirichlet boundary conditions of the navier stokes equations the schemes all have second order accuracy for both straight and curved boundaries the accuracy and stability of two specific schemes are examined through several numerical experiments the results validate the second order accuracy and show that a boundary scheme with a convex combination of distribution functions has better stability

incompressible limits of lattice boltzmann equations using multiple relaxation times lattice boltzmann equations using multiple relaxation times are intended to be more stable than those using a single relaxation time the additional relaxation times may be adjusted to suppress non hydrodynamic modes that do not appear directly in the continuum equations but may contribute to instabilities on the grid scale if these relaxation times are fixed in lattice units as in previous work solutions computed on a given lattice are found to diverge in the incompressible small mach number limit this non existence of an incompressible limit is analysed for an inclined one dimensional jet an incompressible limit does exist if the non hydrodynamic relaxation times are not fixed but scaled by the mach number in the same way as the hydrodynamic relaxation time that determines the viscosity

a simple phase field model for interface tracking in three dimensions abstract based on a conservative phase field lattice boltzmann lb method we present a 3d model for tracking an interface in multiphase flows in addition to being mass conserving the main advantage of this lb method is that the collision process is made entirely local by invoking central moments in the calculation of vectors normal to the interface we construct the model on different 3d lattices d3q7 and d3q15 with inherently distinct isotropy properties to test the model we conduct a variety of benchmark studies such as the evolution of an interface in the form of a slotted sphere in a rotational flow field and the evolution of a spherical interface in a vortex flow a deformation flow and a shear flow the results of these benchmarks are compared against the finite difference based version of the lb model in which a non local finite difference scheme is used to calculate the interface normal in terms of error the moment based model while competitive is generally outperformed by the finite difference model despite this the moment based interface tracking model is inherently more efficient and deserves consideration particularly for memory distributed parallel computing we also consider the interaction between a binary fluid and a solid wall and introduce a method to implement the three phase contact angle within this framework the proposed model for dealing with the contact line is simple clean and straightforward to implement and shown to recover desired contact angles very well

lattice boltzmann simulations on irregular grids introduction of the natrium library the lattice boltzmann method is a modern approach to simulate fluid flow in its original formulation it is restricted to regular grids second order discretizations and a unity cfl number this paper describes our new off lattice boltzmann solver natrium an extensible and parallel c code to perform lattice boltzmann simulations on irregular grids natrium also allows high order spatial discretizations and non unity cfl numbers to be used we demonstrate how these features can efficiently decrease the number of grid points required in a simulation and thus reduce the computational time compared to the standard lattice boltzmann method we detail the implementation of a recently proposed semi lagrangian lattice boltzmann method and prove its efficiency in comparisons to other state of the art off lattice boltzmann schemes

acceleration of steady state lattice boltzmann simulations on non uniform mesh using local time step method in this paper the local time step method is applied to the lattice boltzmann method lbm on non uniform grid generalized form of interpolation supplemented lbm gilbm for steady flow simulations the local time step method is known to be an effective technique to accelerate the solution to the converged steady state on non uniform grid first code validation for global time step method is performed by solving flow around a cylinder at low reynolds numbers our results show good agreement with previous studies two dimensional flow simulations around an airfoil were performed in order to validate the code using the local time step method and the results are compared with the global time step solutions the pressure distribution and the aerodynamic coefficients of global and local time step results are in good agreement they are also consistent with the previous studies at the same time cpu time required to obtain the steady state solutions using the local time step are reduced by 70 80 compared with that using global time step

on optimal node spacing for immersed boundary lattice boltzmann method in 2d and 3d abstract a computational study on optimal spacing of lagrangian nodes discretizing a rigid and immobile immersed body boundary in 2d and 3d is presented in order to show how the density of the lagrangian points affects the numerical results of the immersed boundary lattice boltzmann method ib lbm the study is based on the implicit velocity correction based ib lbm proposed by wu and shu 2009 2010 that allows computing the fluid body interaction force however the original method fails for densely spaced lagrangian points due to ill conditioned or even singular linear systems that arise from the derivation of the method we propose a modification that improves the solvability of the linear systems and compare the performance of both methods using several benchmark problems the results show how the spacing of the lagrangian points affects the numerical results mainly the permeability of the discretized body boundary in applications to fluid flows over rigid obstacles and blood flows in arteries in 2d and 3d

asymptotic analysis of multiple relaxation time lattice boltzmann schemes for mixture modeling a new lattice boltzmann model for simulating ideal mixtures has been developed by means of the multiple relaxation time mrt approach when compared with the previous single relaxation time srt formulation of the same model based on the continuous kinetic theory the new model offers the possibility to independently tune the mutual diffusivity and the effects of cross collisions on the effective stress tensor the additional degrees of freedom due to the increased set of relaxation time constants used for modeling the cross collisions allow us to match the experimental data on macroscopic transport coefficients two different integration rules i e the forward euler and the modified mid point integration rule were used in order to numerically integrate the developed model unfortunately the simpler forward euler integration rule violates the mass conservation and there is no way to fix the problem by changing the definition of the macroscopic velocity on the other hand a small correction has been purposely designed for compensating this error by means of the mid point integration rule some numerical simulations are reported for proving the effectiveness of the proposed corrective factor for the considered application the asymptotic analysis recently suggested as an effective tool for analyzing the macroscopic equations corresponding to the lattice boltzmann schemes offers a remarkable advantage in comparison with the classical chapman enskog technique because it easily deals with leading terms in the distribution functions which are no more maxwellian

designing correct fluid hydrodynamics on a rectangular grid using mrt lattice boltzmann approach while the lattice boltzmann method lbm has become a powerful numerical approach for solving complex flows the standard lattice boltzmann method typically uses a square lattice grid in two spatial dimensions and cubic lattice grid in three dimensions for inhomogeneous and anisotropic flows it is desirable to have a lbm model that utilizes a rectangular grid there were two previous attempts to extend the multiple relaxation time mrt lbm to a rectangular lattice grid in 2d however the resulting hydrodynamic momentum equation was not fully consistent with the navier stokes equation due to anisotropy of the transport coefficients in the present work a new mrt model with an additional degree of freedom is developed in order to match precisely the navier stokes equation when a rectangular lattice grid is used we first revisit the previous attempts to understand the origin and nature of anisotropic transport coefficients by conducting an inverse design analysis within the chapman enskog procedure then an additional adjustable parameter that governs the relative orientation in the energy normal stress subspace is introduced it is shown that this adjustable parameter can be used to fully eliminate the anisotropy of transport coefficients thus the exact navier stokes equation can be derived on a rectangular grid our theoretical findings are confirmed by numerical solutions using three two dimension benchmark problems i e the channel flow the cavity flow and the decaying taylor green vortex flow the numerical results demonstrate that the proposed model shows remarkably good performance with appropriate choice of model parameters

reduced passage method for multirow forced response computations this paper presents a time domain fourier method for modeling steady and unsteady nonaxisymmetric flows in turbomachinery on a reduced computational domain the method extends well established single passage multirow methods which efficiently model periodic unsteadiness in single stages to assemblies with stationary circumferential perturbations with periodicity different from the blade count such perturbations are caused for example by rotor rotor stator stator interaction or geometric circumferential variations the method is therefore suitable to study low engine order forcing problems flow past nonuniform assemblies and clocking problems the proposed method solves the flow inside several discrete passages located at different circumferential positions using a time accurate scheme boundary conditions at the azimuthal and interrow surfaces are approximated via time space fourier series and couple the individual passages the reduced passage model is validated against the whole annulus solutio

one point boundary condition for the lattice boltzmann method we propose a correction to the bounce back boundary condition for lattice boltzmann algorithms which improves the accuracy of pressure from zero to first order and the accuracy of velocity from first to second order compared to interpolation based corrections our method has the advantage of being completely local in fact methods using interpolation face difficulties at boundary points where not enough neighboring nodes are available we show that a combination with our method offers a natural solution to this problem

cascaded digital lattice boltzmann automata for high reynolds number flow lattice boltzmann methods are of limited applicability for direct numerical simulation of turbulent flow due to instabilities in the zero viscosity limit we observe that this is caused by an insufficient degree of galilean invariance of the relaxation type lattice boltzmann collision operator the cascaded digital lattice boltzmann automata described here provides a method with which to achieve stable collision operators down to the limit of zero viscosity

a characteristic galerkin method for discrete boltzmann equation abstract the characteristic galerkin finite element method for the discrete boltzmann equation is presented to simulate fluid flows in complex geometries the inherent geometric flexibility of the finite element method permits the easy use of simple cartesian variables on unstructured meshes and the mesh clustering near large gradients the characteristic galerkin procedure with appropriate boundary condition results in accurate solutions with little numerical diffusion several test cases are conducted including unsteady couette flows lid driven cavity flows and steady flow past a circular cylinder on unstructured meshes the numerical results are in good agreement with previous analytical if applicable numerical and experimental results

lattice boltzmann method for 3 d flows with curved boundary in this work we investigate two issues that are important to computational efficiency and reliability in fluid dynamic applications of the lattice boltzmann equation lbe 1 computational stability and accuracy of different lattice boltzmann models and 2 the treatment of the boundary conditions on curved solid boundaries and their 3 d implementations three athermal 3 d lbe models q15d3 q19d3 and q27d3 are studied and compared in terms of efficiency accuracy and robustness the boundary treatment recently developed by filippova and hanel 1998 j comp phys 147 219 and mei et al 1999 j comp phys 155 307 in 2 d is extended to and implemented for 3 d the convergence stability and computational efficiency of the 3 d lbe models with the boundary treatment for curved boundaries were tested in simulations of four 3 d flows 1 fully developed flows in a square duct 2 flow in a 3 d lid driven cavity 3 fully developed flows in a circular pipe and 4 a uniform flow over a sphere we found that while the 15 velocity 3 d q15d3 model is more prone to numerical instability and the q27d3 is more computationally intensive the q19d3 model provides a balance between computational reliability and efficiency through numerical simulations we demonstrated that the boundary treatment for 3 d arbitrary curved geometry has second order accuracy and possesses satisfactory stability characteristics

multistage coupling for unsteady flows in turbomachinery in this paper we present the a three dimensional time linearized unsteady euler solver for computing unsteady flows in multistage turbomachines using this approach each blade row is modeled with a computational grid spanning a single blade passage within each blade passage several time linearized un steady solutions are computed one for each of several spinning modes re tained in the model each spinning mode has its own frequency and interblade phase angle these various solutions are coupled together at the inter row bound aries between the blade rows results are presented for several geometries and demonstrate the accuracy and efficiency of the method as well as the impor tance of multistage effects in particular we show that multistage effects can strongly affect the aerodynamic loads acting on a given blade row further more the method presented is highly efficient for example to perform a flutter calculation requires only about three times the cpu time of one steady flow computation for each interblade phase angle and frequency considered

numerics of the lattice boltzmann method effects of collision models on the lattice boltzmann simulations we conduct a comparative study to evaluate several lattice boltzmann lb models for solving the near incompressible navier stokes equations including the lattice boltzmann equation with the multiple relaxation time mrt the two relaxation time trt the single relaxation time srt collision models and the entropic lattice boltzmann equation elbe the lid driven square cavity flow in two dimensions is used as a benchmark test our results demonstrate that the elbe does not improve the numerical stability of the srt or the lattice bhatnagar gross krook lbgk model our results also show that the mrt and trt lb models are superior to the elbe and lbgk models in terms of accuracy stability and computational efficiency and that the elbe scheme is the most inferior among the lb models tested in this study thus is unfit for carrying out numerical simulations in practice our study suggests that to optimize the accuracy stability and efficiency in the mrt model it requires at least three independently adjustable relaxation rates one for the shear viscosity ensuremath nu or the reynolds number text re one for the bulk viscosity ensuremath zeta and one to satisfy the criterion imposed by the dirichlet boundary conditions which are realized by the bounce back type boundary conditions

nonhydrodynamic modes and a priori construction of shallow water lattice boltzmann equations lattice boltzmann equations for the isothermal navier stokes equations have been constructed systematically using a truncated moment expansion of the equilibrium distribution function from continuum kinetic theory applied to the shallow water equations with its different equation of state the same approach yields discrete equilibria that are subject to a grid scale computational instability different and stable equilibria were previously constructed by salmon j marine res 57 503 1999 the two sets of equilibria differ through a nonhydrodynamic or ghost mode that has no direct effect on the hydrodynamic behavior derived in the slowly varying limit however salmon s equilibria eliminate a coupling between hydrodynamic and ghost modes one that leads to instability with a growth rate increasing with wave number previous work has usually assumed that truncated moment expansions lead to stable schemes such instabilities have implications for lattice boltzmann equations that simulate other nonideal equations of state or that simulate fully compressible nonisothermal fluids using additional particles

parametrization of the cumulant lattice boltzmann method for fourth order accurate diffusion part ii the optimized cumulant lattice boltzmann method with fourth order accurate diffusion is used to simulate the flow around a sphere up to reynolds number 106 the drag crisis is well captured by the method we demonstrate with our results that the drag crisis corresponds to an almost discrete jump in the flow conditions the intermediate values of drag in a small range of reynolds numbers around the drag crisis observed in averaged data sets are found to originate from the flow switching between the high and the low drag conditions around the critical reynolds number the time spent in the low drag condition increases with the reynolds number such that the average drag curve has a finite steepness we demonstrate that the cumulant lattice boltzmann model with optimized parameters captures the drag crisis for flows over a sphere no sub grid model and no wall function is required and the boundary layer is only marginally resolved it is observed that in the transition regime between the high and the low drag configuration the flow switches from one state to the other state

near wall treatment for the simulation of turbulent flow by the cumulant lattice boltzmann method abstract we present a new wall function implementation for the cumulant lattice boltzmann method that sets a partial slip velocity on the wall by computing a skin frictional coefficient our approach uses local information and is particularly appropriate for implementations on general purpose graphics processing units the validation of the model has been conducted by performing numerical simulations of the turbulent channel flow test case with different grid resolutions and for different reynolds numbers the results showed encouraging agreement with direct numerical simulation data for velocity profile reynolds shear and normal stresses

truncation errors and the rotational invariance of three dimensional lattice models in the lattice boltzmann method abstract the application of the lattice boltzmann method lbm in three dimensional isothermal hydrodynamic problems often adopts one of the following models d3q15 d3q19 or d3q27 although all of them retrieve consistent navier stokes dynamics in the continuum limit they are expected to behave differently at discrete level the present work addresses this issue by performing a lbm truncation error analysis as a conclusion it is theoretically demonstrated that differences among the aforementioned cubic lattices lie in the structure of their non linear truncation errors while reduced lattice schemes such as d3q15 and d3q19 introduce spurious angular dependencies through non linear truncation errors the complete three dimensional cubic lattice d3q27 is absent from such features this result justifies the superiority of the d3q27 lattice scheme to cope with the rotational invariance principle in three dimensional isothermal hydrodynamic problems particularly when convection is not negligible such a theoretical conclusion also finds support in numerical tests presented in this work a poiseuille duct flow and a weakly rotating duct flow

grid refinement for lattice bgk models lattice boltzmann models proposed at the end of the 1980s as the noise free version of lattice gas models are based on gas kinetic representation of fluid flow their recent modifications the lattice bgk models provide especially simple effective and stable algorithms for the solution of hydrodynamical problems a local second order grid refinement scheme for the lattice bgk model is proposed in this work the refinement scheme and a boundary fitting scheme for complicated geometries are applied to simulate a benchmark problem of flow past a cylinder in a channel with small and moderate reynolds numbers

volumetric formulation of the lattice boltzmann method for fluid dynamics basic concept a lattice boltzmann algorithm based on a volumetric representation is formulated for achieving properties consistent with the standard form at finer resolution in contrast to pointwise interpolation schemes this approach can be applied to arbitrary meshes without compromising exact conservation or equilibrium properties

flow simulation around cambered airfoil by using conformal mapping and intermediate domain in lattice boltzmann method in this paper the developed interpolation lattice boltzmann method is used for simulation of unsteady fluid flow it combines the desirable features of the lattice boltzmann and the joukowski transformation methods this approach has capability to simulate flow around curved boundary geometries such as airfoils in a body fitted grid system simulation of unsteady flow around a cambered airfoil in a non uniform grid for the first time is considered to show the capability of this method for modeling of fluid flow around complex geometries and complicated long term periodic flow phenomena the developed solver is also coupled with a fast adaptive grid generator in addition the new approach retains all the advantages of the standard lattice boltzmann method the strouhal number the pressure the drag and the lift coefficients obtained from the simulations agree well with classical computational fluid dynamics simulations numerical studies for various test cases illustrate the strength of this new approach

theory and applications of an alternative lattice boltzmann grid refinement algorithm this contribution proposes an alternative lattice boltzmann grid refinement algorithm that overcomes the drawbacks that plague existing approaches we demonstrate that this algorithm is accurate and applicable for all values of the relaxation time we also show that this algorithm can significantly speed up the flow settlement process by using a hierarchy of grid levels the stationary regime can be approached up to a thousand times faster than with a single grid resolution

cross terms analysis in the modified instantaneous power spectrum this correspondence examines cross terms in the modified version of the instantaneous power spectrum mips which is a smoothed form of the real part of the rihaczek distribution mips was reported recently to be less sensitive to the poor resolution of spectro gram and the cross terms in the pseudo wigner ville distribution pwvd however in this correspondence we will show that like pwvd the mips possesses cross terms too the only differences be tween them are the location and the oscillating frequency of the cross terms we deduce that the cross terms of the mips are located in about the same region of the autoterms while the cross terms of the wvd are located midway between the autoterms the undesirable cross terms and artifact between different spectral components are much less se vere and interfere less with each other in mips than in pwvd cases i introduction page originally defined the instantaneous power specturm ips as the derivative of the running energy spectrum i which satis fied many of the properties of time frequency distribution how ever its ringing effect blocks its application hippenstiel and de oliveira 2 advocated the use of the fourier transform of an av eraged correlation function estimate this estimate is further mod ified by applying a sliding window after forming the correlation estimate the result a smoothed version of the real part of the rihaczek distribution 3 is a modified version of ips hippenstiel shows that the mips can be less sensitive to the time frequency resolution tradeoff problem occurring in the spectrogram 141 and the cross term interference problem occurring in wigner ville dis tribution wvd 5 7 moreover the modified ips mips can avoid the ringing effect which is a major problem in page s ips method however in this correspondence we will show that like pwvd the mips possesses cross terms too compared with wvd the only differences between them are the location and the oscil lating frequency of the cross terms this correspondence will also show why the modified ips reduces the ringing effect

viscosity independent numerical errors for lattice boltzmann models from recurrence equations to magic collision numbers we prove for generic steady solutions of the lattice boltzmann lb models that the variation of the numerical errors is set by specific combinations called magic numbers of the relaxation rates associated with the symmetric and anti symmetric collision moments given the governing dimensionless physical parameters such as the reynolds or peclet numbers and the geometry of the computational mesh the numerical errors remain the same for any change of the transport coefficients only when the free kinetic anti symmetric rates and the boundary rules are chosen properly the single relaxation time bgk model has no free collision rate and yields viscosity dependent errors with any boundary scheme for hydrodynamic problems the simplest and most efficient collision operator for invariant errors is the two relaxation times trt model as an example this model is able to compute viscosity independent permeabilities for any porous structure these properties are derived from steady recurrence equations obtained through linear combinations of the lb evolution equations in which the equilibrium and non equilibrium components are directly interconnected via finite difference link wise central operators the explicit dependency of the non equilibrium solution on the relaxation rates is then obtained this allows us first to confirm the governing role of the magic combinations for steady solutions of the stokes equation second to extend this property to steady solutions of the navier stokes and anisotropic advection diffusion equations third to develop a parametrization analysis of the microscopic and macroscopic closure relations prescribed via link wise boundary schemes

multiple relaxation time lattice boltzmann method for immiscible fluids at high reynolds numbers the lattice boltzmann method for immiscible multiphase flows with large density ratio is extended to high reynolds number flows using a multiple relaxation time mrt collision operator and its stability and accuracy are assessed by simulating the kelvin helmholtz instability the mrt model is successful at damping high frequency oscillations in the kinetic energy emerging from traveling waves generated by the inclusion of curvature numerical results are shown to be in good agreement with prior studies using adaptive mesh refinement techniques applied to the navier stokes equations effects of viscosity and surface tension as well as density ratio are investigated in terms of the reynolds and weber numbers it is shown that increasing the reynolds number results in a more chaotic interface evolution and eventually shattering of the interface while surface tension is shown to have a stabilizing effect

lattice boltzmann method on curvilinear coordinates system using an interpolation based strategy the lattice boltzmann method is extended to apply to general curvilinear coordinate systems as an example a cylindrical coordinate system is used to simulate two dimensional flow around a circular cylinder numerical simulations are carried out for impulsive initial conditions with reynolds numbers up to 104 the agreement of our results with previous computational and experimental results is satisfactory compared with previous lattice boltzmann simulations of the same problem our new approach greatly enhances the computational efficiency

the cumulant lattice boltzmann equation in three dimensions theory and validation we propose analyze and validate a lattice boltzmann model with a cumulant collision operator the new model is analytically and numerically shown to poses smaller errors than a moment based multiple relaxation time lattice boltzmann model we demonstrate the usability of the cumulant lattice boltzmann model by simulations of flow around a sphere for reynolds numbers from 200 to 105

lattice boltzmann hydrodynamics of single square grid generated turbulence a partial entropic stabilisation approach abstract under resolved direct numerical simulations of turbulence in the wake of a single square grid ssg are conducted using the lattice boltzmann method lbm with varying degrees of partial moment entropic stabilisation turbulence statistics along the grid centreline show satisfactory agreement with literature greatly outperforming a control study employing the single relaxation time smagorinsky les model with equivalent resolution the coarse resolution entropic lbm simulations are able to capture the qualitative behaviour of the anisotropic and non homogeneous turbulence generated by the ssg indicating possible extension of the capability of the entropic lattice boltzmann method to simulate more exotic forms of turbulence beyond those reported by the majority of current studies however in the extreme near field of the single square grid pseudo compressibility effects even at a low lattice mach number undermine lbm predictions for turbulence which is generated by action of the pressure hessian this is found to be an issue for all models studied and not a numerical artefact of the entropic stabilisation with regard to the action of the entropic stabiliser a comparison of models employing differing degrees of stabilisation on higher order natural moments suggest that the trace of the stress tensor should not be subject to entropic control for better accuracy in turbulence prediction

asymptotic analysis of the lattice boltzmann equation in this article we analyze the lattice boltzmann equation lbe by using the asymptotic expansion technique we first relate the lbe to the finite discrete velocity model fdvm of the boltzmann equation with the diffusive scaling the analysis of this model directly leads to the incompressible navier stokes equations as opposed to the compressible navier stokes equations obtained by the chapman enskog analysis with convective scaling we also apply the asymptotic analysis directly to the fully discrete lbe as opposed to the usual practice of analyzing a continuous equation obtained through the taylor expansion of the lbe this leads to a consistency analysis which provides order by order information about the numerical solution of the lbe the asymptotic technique enables us to analyze the structure of the leading order errors and the accuracy of numerically derived quantities such as vorticity it also justifies the use of richardson s extrapolation method as an example a two dimensional taylor vortex flow is used to validate our analysis the numerical results agree very well with our analytic predictions

a consistent grid coupling method for lattice boltzmann schemes a method of coupling grids of different mesh size is developed for classical lattice boltzmann lb algorithms on uniform grids the approach is based on an asymptotic analysis revealing suitable quantities equalized along the grid interfaces for exchanging information between the subgrids in contrast to other couplings the method works without overlap zones moreover the grid velocity mach number is not kept constant as the time step depends not linearly but quadratically on the grid spacing to illustrate the basic idea we use a simple lb algorithm solving the advection diffusion equation the proposed grid coupling is validated by numerical convergence studies indicating that the coupling does not affect the second order convergence behavior of the lb algorithm which is observed on uniform grids in order to demonstrate its principal applicability to other lb models the coupling is generalized to the standard d2p9 model for navier stokes flow and tested numerically as we use analytic tools different from the chapman enskog expansion the theoretical background material is given in two appendices in particular the results of numerical experiments are confirmed with a consistency analysis

a cascaded phase field lattice boltzmann model for the simulation of incompressible immiscible fluids with high density contrast abstract in this work a conservative phase field model for the simulation of immiscible multiphase flows is developed using an incompressible velocity based cascaded lattice boltzmann method clbm extensions are made to the lattice boltzmann lb equations for interface tracking and incompressible hydrodynamics proposed by fakhari et al 1 by performing relaxation operations in central moment space this was motivated by the work of fei et al 2 3 where promising results from such a transformation were observed the relaxation of central moments is defined in a reference frame moving with the fluid while the existing multiple relaxation time 4 5 scheme performs collision in a fixed frame of reference moreover the derivations make use of continuous maxwellian distribution functions as a result the clbm enhances the galilean invariance and stability of the method when high lattice mach numbers are evident the cascaded scheme has been previously used in the literature to simulate multiphase flows based on the pseudo potential model where it allowed for high density and viscosity contrasts to be captured 6 7 here the clbm is implemented within the phase field framework and is verified through the analysis of a layered poiseuille flow the performance of the clbm is then investigated in terms of spurious currents galilean invariance and computational efficiency finally the work of fakhari et al 1 is extended by validating the model s ability to capture the relation between surface tension and the rise velocity of a planar taylor bubble in both stagnant and flowing fluids new counter current results indicate that the rise velocity model of ha ngoc and fabre 8 also applies in this regime

simulation of rotating objects in fluids with the cumulant lattice boltzmann model on sliding meshes abstract in this paper a rotating grid technique for the cumulant lattice boltzmann model is presented the rotating object is embedded in a rotating mesh that communicates with an enclosing stationary mesh via compact quadratic interpolation on the rotating mesh coriolis and centrifugal forces model the rotation with respect to the outer eulerian frame of reference a proper rotation of all moments is imposed in the interface between the moving and the static grid the fluid flow is simulated by the cumulant lattice boltzmann model profiles of pressure velocity and shear stress are compared with the analytical solution of taylor couette flow and we demonstrate that our scheme is second order accurate in space as a second numerical benchmark lift and drag coefficients for a rotating ellipsoidal cylinder in a laminar flow are simulated and successfully compared to a reference solution

numerical simulation of viscous flow over non smooth surfaces the incompressible viscous flow over several non smooth surfaces is simulated numerically by using the lattice boltzmann method a numerical strategy for dealing with a curved boundary with second order accuracy for velocity field is presented the drag evaluation is performed by the momentum exchange method the streamline contours are obtained over surfaces with different shapes including circular concave circular convex triangular concave triangular convex regular sinusoidal wavy and irregular sinusoidal wavy are obtained the flow patterns are discussed in detail the velocity profiles over different kinds of non smooth surfaces are investigated the numerical results show that the lattice boltzmann method is reliable accurate easy to implement and can provide valuable help for some engineering practices

time varying spectral estimation using the instantaneous power spectrum ips the spectral content of time varying signals is examined using a modified version of the instantaneous power spectrum ips the short duration periodogram and the pseudo wigner ville distribution pwd have been used extensively to display the time varying spectral information a disadvantage of the periodogram is its inherently poor resolution due to the requirement of matching the resolution width to the spectral dynamics of the signal potential problems associated with pwd are spectral cross terms and an inability to resolve spectral components at the endpoints of the analysis segment a modified version of ips is shown to be less sensitive to these types of problems in addition ips can work with real valued signals sampled at the traditional nyquist rate

improving the low mach number steady state convergence of the cascaded lattice boltzmann method by preconditioning abstract cascaded lattice boltzmann method lbm involves the use of central moments in a multiple relaxation time formulation in prescribing the collision step when the goal is to simulate low mach number stationary flows the greater the disparity between the magnitude of fluid speed and the sound speed the higher is the numerical stiffness which results in relatively large number of time steps for convergence of the lbm one way to improve the steady state convergence of the scheme is to precondition the cascaded lbm which reduces the disparities between the characteristic speeds or equivalently those between the eigenvalues of the system in this paper we present a new preconditioned two dimensional cascaded lbm where a preconditioning parameter is introduced into the equilibrium moments as well as the forcing terms particular focus is given to preconditioning differently the moments due to forcing at first and second orders so as to avoid any spurious effects in the emergent macroscopic equations a chapman enskog analysis performed on this approach shows consistency to the preconditioned navier stokes equations this modified central moment based scheme is then validated for accuracy by comparison against prior analytical or numerical results for certain benchmark problems including those involving spatially variable body forces finally significant steady state convergence acceleration of the preconditioned cascaded lbm is demonstrated for a set of characteristic parameters

an investigation into curved and moving boundary treatments in the lattice boltzmann method curved boundary treatments provide a means of improving the computational accuracy of the conventional stair shaped approximation used in lattice boltzmann lb simulations furthermore curved boundary treatments can be extended to the modeling of moving boundary problems simply by adding a momentum term to the bounced distribution functions at the solid surface this study commences by investigating three conventional interpolating treatments for curved boundaries in lb problems namely the filippova and hanel fh model o filippova d hanel grid refinement for lattice bgk models j comput phys 147 1998 219 228 bouzidi s model m bouzidi m firdaouss p lallemand momentum transfer of a boltzmann lattice fluid with boundaries phys fluids 13 11 2001 3452 3459 and yu s model d yu r mei w shyy a unified boundary treatment in lattice boltzmann method aiaa 2003 0953 new york 2003 previous investigations have indicated that the interpolations would break the mass conservation at the boundaries since the inaccuracy in evaluation of the momentum transfer at boundary leads to a net mass flux based on this reason a concept of the interpolation free treatment for modeling the curved and moving boundary conditions is proposed to overcome the drawback of these interpolation based curved boundary treatments in present study two interpolation free models are then proposed namely on site interpolation free osif and composite interpolation free cpif models these proposed models are initially applied to simulate the flow in the channels containing a stationary square block positioned at various locations along the longitudinal axis the simulations results are then compared with those obtained using the three conventional interpolating treatments the interpolation free models are then applied to the case of moving boundary problems in which a square block and a cylindrical block respectively move with a constant speed along a channel containing stationary flows to test the galilean effect of the proposed cpif model a couette flow past the stationary square cylinder block with the moving top bottom walls is simulated overall the numerical results show that the proposed interpolation free curved treatment models significantly improve the accuracy of the mass flux computation near the solid surface and thus enhance the accuracy of the momentum interaction at the moving boundaries

a central moments based lattice boltzmann scheme for shallow water equations abstract in this paper we explore the possibility to derive an original lattice boltzmann scheme for solving shallow water equations specifically it is proposed to decompose the collision operator by means of a non orthogonal basis of central moments which relax independently to a discrete equilibrium our method is strictly consistent with the bgk operator as the latter is recovered exactly if all the moments relax with a common frequency the methodology is validated against five well consolidated established benchmark problems showing very good agreement moreover it possesses very high properties in terms of stability

dynamically adaptive lattice boltzmann simulation of shallow water flows with the peano framework we present a dynamically adaptive lattice boltzmann lb implementation for solving the shallow water equations swes our implementation extends an existing lb component of the peano framework we revise the modular design with respect to the incorporation of new simulation aspects and lb models the basic swe lb implementation is validated in different breaking dam scenarios we further provide a numerical study on stability of the mrt collision operator used in our simulations

lattice boltzmann method on composite grids a composite block structured lattice boltzmann method is proposed for the simulation of two dimensional incompressible fluid flows the grid structure is composed of a coarse base grid and one or several fine grid s the former covers the entire physical domain the latter are placed at regions where local grid refinement is desirable the simulation is first carried out on the base grid level at a smaller relaxation time allowing a rapid propagation of boundary information throughout the entire domain thus large scale flow features can be resolved efficiently at a relatively low cost at a later time fine grid variables are initiated the dependent variables on both grid levels are then advanced in time simultaneously with the fine grid boundary conditions obtained from the base grid solution at the grid interface as a demonstration the lid driven cavity flow is selected for study the results show good agreement with benchmark numerical data and those calculated from the finite volume u 2 mathrm rans model the proposed method is able to produce accurate solutions on fine grids with a considerable saving in cpu time

quartic parameters for acoustic applications of lattice boltzmann scheme using the taylor expansion method we show that it is possible to improve the lattice boltzmann method for acoustic applications we derive a formal expansion of the eigenvalues of the discrete approximation and fit the parameters of the scheme to enforce fourth order accuracy the corresponding discrete equations are solved with the help of symbolic manipulation the solutions are obtained in the case of d3q27 lattice boltzmann scheme various numerical tests support the coherence of this approach

diffuse interface modeling of three phase contact line dynamics on curved boundaries we introduce a simple and efficient lattice boltzmann method for immiscible multiphase flows capable of handling large density and viscosity contrasts the model is based on a diffuse interface phase field approach within this context we propose a new algorithm for specifying the three phase contact angle on curved boundaries within the framework of structured cartesian grids the proposed method has superior computational accuracy compared with the common approach of approximating curved boundaries with stair cases we test the model by applying it to four benchmark problems i wetting and dewetting of a droplet on a flat surface and ii on a cylindrical surface iii multiphase flow past a circular cylinder at an intermediate reynolds number and iv a droplet falling on hydrophilic and superhydrophobic circular cylinders under differing conditions where available our results show good agreement with analytical solutions and or existing experimental data highlighting strengths of this new approach

multireflection boundary conditions for lattice boltzmann models we present a general framework for several previously introduced boundary conditions for lattice boltzmann models such as the bounce back rule and the linear and quadratic interpolations the objectives are twofold first to give theoretical tools to study the existing link type boundary conditions and their corresponding accuracy second to design boundary conditions for general flows which are third order kinetic accurate using these new boundary conditions couette and poiseuille flows are exact solutions of the lattice boltzmann models for a reynolds number mathrm re 0 stokes limit for arbitrary inclination with the lattice directions numerical comparisons are given for stokes flows in periodic arrays of spheres and cylinders linear periodic array of cylinders between moving plates and for navier stokes flows in periodic arrays of cylinders for mathrm re l200 these results show a significant improvement of the overall accuracy when using the linear interpolations instead of the bounce back reflection up to an order of magnitude on the hydrodynamics fields further improvement is achieved with the new multireflection boundary conditions reaching a level of accuracy close to the quasianalytical reference solutions even for rather modest grid resolutions and few points in the narrowest channels more important the pressure and velocity fields in the vicinity of the obstacles are much smoother with multireflection than with the other boundary conditions finally the good stability of these schemes is highlighted by some simulations of moving obstacles a cylinder between flat walls and a sphere in a cylinder

implementation of the compact interpolation within the octree based lattice boltzmann solver musubi abstract a sparse octree based parallel implementation of the lattice boltzmann method for non uniform meshes is presented in this paper to couple grids of different resolutions a second order accurate compact interpolation is employed and further extended into three dimensions the compact interpolation requires only four source elements from the adjacent level for both two and three dimensions thus improves the computational efficiency moreover a weight based domain decomposition algorithm and the level wise arrangement of elements is explained in detail the second order convergence for both velocity and strain rate are validated numerically in the taylor green vortex test case additionally the 3d flow around a sphere in the reynolds number range of 100 1000 is investigated good agreement between simulated results and those from literature is observed which provides further evidence for the accuracy of our method