scaling of boldsymbol mathcal p mathcal t asymmetries in viscous flow with boldsymbol mathcal p mathcal t symmetric inflow and outflow in recent years open systems with balanced loss and gain that are invariant under the combined parity and time reversal operations have been studied via asymmetries of their solutions they represent systems as diverse as coupled optical waveguides and electrical or mechanical oscillators we numerically investigate the asymmetries of incompressible viscous flow in two and three dimensions with balanced inflow outflow symmetric configurations by introducing configuration dependent classes of asymmetry functions in velocity kinetic energy density and vorticity fields we find that the flow asymmetries exhibit power law scaling with a single exponent in the laminar regime with the reynolds number ranging over four decades we show that such single exponent scaling is expected for small reynolds numbers although its robustness at large values of reynolds numbers is unexpected our results imply that symmetric inflow outflow configurations provide a hitherto unexplored avenue to tune flow properties

existence theorems for nonselfadjoint semilinear elliptic boundary value problems where e is a real elliptic linear differential operator in a bounded domain g of r with a given system of linear homogeneous conditions say bx 0 on the boundary ag of g and where n is a nemitsky type nonnecessarily linear operator we shall make use here of the alternative method and particularly we shall make use for the elliptic case of new remarks these remarks suggest that both the auxiliary and bifurcation equations can be analyzed under different topologies and by a more specific construction of the operator s y0 x0 actually some of these remarks have been already used implicitly in previous papers on the semilinear wave equation in r2 cesari and kannan 5 cesari and pucci 6 for selfadjoint elliptic problems landesman and lazer 9 proved also by the alternative method a remarkable theorem which was then extended by williams 14 by the same method and by others by different arguments later shaw 12 proved again by the alternative method that landesman s and lazer s theorem extends even to nonselfadjoint problems with equal fredholm indices and whose eigenfunctions share regions of positivity and negativity with their corresponding adjoint eigenfunctions in the present paper we definitely aim at elliptic problems which are not necessarily selfadjoint and do not necessarily satisfy shaw s requirements the sufficient conditions we obtain are more quantitative in character and concern the cases nx f t g t d x and nx f f g t x t t e g however as we show by examples for the case nx f t g t x t our sufficient conditions for existence allow a great freedom on g on which no monotonicity is required

asymptotic analysis of extrapolation boundary conditions for lbm we present an investigation of extrapolation boundary conditions for lattice boltzmann method lbm using asymptotic analysis equilibrium and non equilibrium extrapolation methods for velocity and pressure boundary conditions proposed in the literature were tested numerically in specific cases we analyse these boundary conditions using asymptotic expansion techniques and show an improvement in the accuracy of the lattice boltzmann solution we also present few numerical examples and simulate fluid flow across an unsymmetrically placed stationary cylinder in a channel with steady and unsteady flow conditions thus the article demonstrates application of asymptotic analysis to understand properties of extrapolation boundary conditions for lbm and show the flexibility of these boundary conditions for complex fluid flow applications

a new differential lattice boltzmann equation and its application to simulate incompressible flows on non uniform grids a new differential lattice boltzmann equation lbe is presented in this work which is derived from the standard lbe by using taylor series expansion only in spatial direction with truncation to the second order derivatives the obtained differential equation is not a wave like equation when a uniform grid is used the new differential lbe can be exactly reduced to the standard lbe the new differential lbe can be applied to solve irregular problems with the help of coordinate transformation the present scheme inherits the merits of the standard lbe the 2 d driven cavity flow is chosen as a test case to validate the present method favorable results are obtained and indicate that the present scheme has good prospects in practical applications

numerical stability of explicit off lattice boltzmann schemes the off lattice boltzmann olb method consists of numerical schemes which are used to solve the discrete boltzmann equation unlike the commonly used lattice boltzmann method the spatial and time steps are uncoupled in the olb method in the currently proposed schemes which can be broadly classified into runge kutta based and characteristics based the size of the time step is limited due to numerical stability constraints in this work we systematically compare the numerical stability of the proposed schemes in terms of the maximum stable time step in line with the overall lb method we investigate the available schemes where the advection approximation is explicit and the collision approximation is either explicit or implicit the comparison is done by implementing these schemes on benchmark incompressible flow problems such as taylor vortex flow poiseuille flow and lid driven cavity flow it is found that the characteristics based olb schemes are numerically more stable than the runge kutta based schemes additionally we have observed that with respect to time step size the scheme proposed by bardow et al 2006 1 is the most numerically stable and computationally efficient scheme compared to similar schemes for the flow problems tested here

nonlinear structural response of laminated composite plates subjected to blast loading we are concerned with the theoretical analysis of the laminated composite plates exposed to normal blast shock waves as well as presenting correlation between the theoretical analysis and the experimental results of the strain time histories the laminated composite plate is clamped at all edges on the theoretical side of the study dynamic equations of the plates are derived by the use of the virtual work principle within the framework of the love theory of plates the geometric nonlinearity effects are taken into account with von karman assumptions then the governing equations of the laminated plate are solved by the runge kutta verner method a new displacement function is considered for the theoretical solution of the blast loaded clamped plate furthermore finite element modeling and analysis for the blast loaded composite plates are presented on the experimental side of the study tests have been carried out on the laminated composite plates with clamped edges for two different blast loads the results of theoretical and finite element methods are compared with the experimental results theoretical and finite element analyses results are in a good agreement there is a qualitative agreement between the analyses and experimental results in the first load case the predicted peak strains and response frequency are in an agreement with the experimental results for first load case thus the theoretical solution may be used for providing material in the preliminary design stage there is a difference between the analysis and experimental results in the second load case because of the extremely large deflections in this study the effects of loading conditions geometrical properties and material properties are separately examined on the dynamic behavior as well

enhanced closure scheme for lattice boltzmann equation hydrodynamics a simple and adaptable closure algorithm for the edge nodes of a lattice boltzmann fluid simulation space is presented its rules are designed to be correct at every instant to maintain local mass and to produce a specified fluid velocity and crucially the correct strain rate tensor at the resulting fluid boundary further our algorithm models the fluid on boundary nodes to the same accuracy as on the bulk nodes and in a demonstrably equivalent manner requiring only a specified boundary velocity the fluid boundary pressure emerging illustrative results for steady and time dependent flows together with outline generalizations are presented

topology optimization in thermal fluid flow using the lattice boltzmann method this paper proposes a topology optimization method for thermal fluid flow problems using the lattice boltzmann method lbm the design sensitivities are derived based on the adjoint lattice boltzmann method albm whose basic idea is that the adjoint problem is first formulated using a continuous adjoint approach and the adjoint problem is then solved using the lbm in this paper the discrete velocity boltzmann equation in which only the particle velocities are discretized is introduced to the albm to deal with the various boundary conditions in the lbm the novel sensitivity analysis is applied in two flow channel topology optimization problems 1 a pressure drop minimization problem and 2 a heat exchange maximization problem several numerical examples are provided to confirm the utility of the proposed method

lattice boltzmann accuracy in pore scale flow simulation we investigate the possibility of using nominally second order accurate techniques for resolving flow about solid boundaries as a means of improving accuracy and reducing grid resolution requirements in pore scale simulations an lbgk method is used to calculate flow in several geometries of increasing complexity using a first order accurate and two nominally second order accurate methods for no slip boundaries the geometries include uniform flow past an isolated sphere quadratic flow past a sphere near a wall flow through a bcc array of spheres and through a randomly packed bed of spheres the packed bed flows are also used to compare hydrodynamic dispersion results the results confirm second order accurate behavior where navier stokes flows are clearly developed however 3d pore scale simulations involve a trade off between resolution of the flow and the number of pore spaces and there is a resolution threshold below which certain flow features such as recirculation are not resolved we conjecture that most simulations will tend to operate near this threshold because of the competing demands for resolution and statistical accuracy we consider local flow features and the velocity distribution in addition to hydraulic permeability and drag to provide a fuller understanding of accuracy near this threshold

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

straight velocity boundaries in the lattice boltzmann method various ways of implementing boundary conditions for the numerical solution of the navier stokes equations by a lattice boltzmann method are discussed five commonly adopted approaches are reviewed analyzed and compared including local and nonlocal methods the discussion is restricted to velocity dirichlet boundary conditions and to straight on lattice boundaries which are aligned with the horizontal and vertical lattice directions the boundary conditions are first inspected analytically by applying systematically the results of a multiscale analysis to boundary nodes this procedure makes it possible to compare boundary conditions on an equal footing although they were originally derived from very different principles it is concluded that all five boundary conditions exhibit second order accuracy consistent with the accuracy of the lattice boltzmann method the five methods are then compared numerically for accuracy and stability through benchmarks of two dimensional and three dimensional flows none of the methods is found to be throughout superior to the others instead the choice of a best boundary condition depends on the flow geometry and on the desired trade off between accuracy and stability from the findings of the benchmarks the boundary conditions can be classified into two major groups the first group comprehends boundary conditions that preserve the information streaming from the bulk into boundary nodes and complete the missing information through closure relations boundary conditions in this group are found to be exceptionally accurate at low reynolds number boundary conditions of the second group replace all variables on boundary nodes by new values they exhibit generally much better numerical stability and are therefore dedicated for use in high reynolds number flows

analysis of lattice boltzmann initialization routines lb simulations can be affected by the arising of initial layers due to an inconsistent initialization of the discrete lb populations we present some previously proposed initialization routines built to overcome that problem using the asymptotic expansion technique we show how their features can be analyzed and in some cases how accuracy and computational efficiency can be improved

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

adjoint based fluid flow control and optimisation with lattice boltzmann methods a lattice boltzmann lb framework to solve fluid flow control and optimisation problems numerically is presented problems are formulated on a mesoscopic basis in a side condition the dynamics of a newtonian fluid is described by a family of simplified boltzmann like equations namely bgk boltzmann equations which are linked to an incompressible navier stokes equation it is proposed to solve the non linear optimisation problem by a line search algorithm the needed derivatives are obtained by deriving the adjoint equations referred to as adjoint bgk boltzmann equations the primal equations are discretised by standard lattice boltzmann methods lbm while for the adjoint equations a novel discretisation strategy is introduced the approach follows the main ideas behind lbm and is therefore referred to as adjoint lattice boltzmann methods albm the corresponding algorithm retains most of the basic features of lb algorithms in particular it enables a highly efficient parallel implementation and thus solving large scale fluid flow control and optimisation problems the overall solution strategy the derivation of a prototype adjoint bgk boltzmann equation the novel albm and its parallel realisation as well as its validation are discussed in detail in this article numerical and performance results are presented for a series of steady state distributed control problems with up to approximately 1 6 million unknown control parameters obtained on a high performance computer with up to 256 processing units

an improved lattice boltzmann method for simulating advective diffusive processes in fluids abstract lattice boltzmann methods are widely used to simulate advective diffusive processes in fluids lattice bhatnagar gross krook methods presented in the literature mostly just exhibit first order spatial accuracy and introduce errors proportional to the velocity squared formulations proposed to alleviate this have only been partly successful and are valid only in certain specific situations we present and demonstrate here a formulation that produces no such second order errors this formulation suggests that a subtle but important adjustment is all it takes to improve the accuracy of the method the key to the improved accuracy of this new model is the non standard definition of the concentration that relates to the distribution function describing the advection diffusion in lattice boltzmann the main advantage of the algorithm comes to view when simulating situations where fluid density variations appear the present formulation of the advection diffusion algorithm will by taking into account these fluid density variations drastically reduce the errors produced compared to the standard formulations we also show how a source term is included in this new formulation without it losing its second order spatial accuracy

alternative kinetic theory based lattice boltzmann model for incompressible axisymmetric flows abstract based on the axisymmetric boltzmann equation an incompressible lattice boltzmann model for axisymmetric flows is proposed within the framework of the kinetic theory based model developed by guo et al 2009 while retaining the advantages of the guo et al 2009 model in terms of the solid physics basis and simple source terms involving no gradient calculations the present model further improves the numerical stability and reduces compressibility errors and computational requirements armed with the assumption that the fluid density is a constant and thus the fluid pressure has no direct relation with the density the incompressibility conditions are realized by applying the hermite expansion then the present model employs a novel way of calculating the fluid pressure which is derived from the modified second order moment equation additionally based on the regularized lattice bgk rlbgk model an extra relaxation parameter pertaining to the ghost mode is introduced to enhance the numerical stability of the present model the accuracy and applicability of the present model are verified by both the chapman enskog theoretical analysis and numerical validations it is demonstrated via well acknowledged test cases that the present model is accurate and reliable for incompressible axisymmetric flows and is able to effectively reduce the compressibility errors vis a vis the guo et al 2009

a hybrid multi time step framework for pore scale and continuum scale modeling of solute transport in porous media abstract in this paper we propose a computational framework which is based on a domain decomposition technique to employ both finite element method which is a popular continuum modeling approach and lattice boltzmann method which is a popular pore scale modeling approach in the same computational domain to bridge the gap across the disparate length and time scales we first propose a new method to enforce continuum scale boundary conditions i e dirichlet and neumann boundary conditions onto the numerical solution from the lattice boltzmann method this method is based on maximization of entropy and preserve the non negativity of discrete distributions under the lattice boltzmann method the proposed computational framework allows different grid sizes orders of interpolation and time steps in different subdomains this allows for different desired resolutions in the numerical solution in different subdomains through numerical experiments the effect of grid and time step refinement disparity of time steps in different subdomains domain partitioning and the number of iteration steps on the accuracy and rate of convergence of the proposed methodology are studied finally to showcase the performance of this framework in porous media applications we use it to simulate the dissolution of calcium carbonate in a porous structure

consistent second order boundary implementations for convection diffusion lattice boltzmann method in this study an alternative second order boundary scheme is proposed under the framework of the convection diffusion lattice boltzmann lb method for both straight and curved geometries with the proposed scheme boundary implementations are developed for the dirichlet neumann and linear robin conditions in a consistent way the chapman enskog analysis and the hermite polynomial expansion technique are first applied to derive the explicit expression for the general distribution function with second order accuracy then the macroscopic variables involved in the expression for the distribution function is determined by the prescribed macroscopic constraints and the known distribution functions after streaming see the paragraph after eq 29 for the discussions of the streaming step in lb method after that the unknown distribution functions are obtained from the derived macroscopic information at the boundary nodes for straight boundaries boundary nodes are directly placed at the physical boundary surface and the present scheme is applied directly when extending the present scheme to curved geometries a local curvilinear coordinate system and first order taylor expansion are introduced to relate the macroscopic variables at the boundary nodes to the physical constraints at the curved boundary surface in essence the unknown distribution functions at the boundary node are derived from the known distribution functions at the same node in accordance with the macroscopic boundary conditions at the surface therefore the advantages of the present boundary implementations are i the locality i e no information from neighboring fluid nodes is required ii the consistency i e the physical boundary constraints are directly applied when determining the macroscopic variables at the boundary nodes thus the three kinds of conditions are realized in a consistent way it should be noted that the present focus is on two dimensional cases and theoretical derivations as well as the numerical validations are performed in the framework of the two dimensional five velocity lattice model

high order finite elements applied to the discrete boltzmann equation a discontinuous galerkin approach for solving the discrete boltzmann equation is presented allowing to compute approximate solutions for fluid flow problems based on a two dimensional high order finite element and an explicit euler time stepping scheme the d2q9 model is discretized and the results are compared to the exact solution of the navier stokes equation four numerical examples are considered including stationary and instationary problems with curved boundaries it is demonstrated that the proposed method allows to obtain the desired highly efficient exponential convergence copyright 2006 john wiley sons ltd

a fully implicit method for lattice boltzmann equations existing approaches for solving the lattice boltzmann equations with finite difference methods are explicit and semi implicit both have certain stability constraints on the time step size in this work a fully implicit second order finite difference scheme is developed we focus on a parallel highly scalable newton krylov ras algorithm for the solution of a large sparse nonlinear system of equations arising at each time step here ras is a restricted additive schwarz preconditioner based on a first order spatial discretization we show numerically that by using the fully implicit method the time step size is no longer constrained by the cfl condition and the newton krylov ras algorithm is scalable on a supercomputer with more than ten thousand processors moreover to calculate the steady state solution we investigate an adaptive time stepping strategy the total compute time required by the implicit method with adaptive time stepping is much smaller than that of an explicit method for several t

momentum transfer correction for macroscopic gradient boundary conditions in lattice boltzmann methods the boundary conditions used to represent macroscopic gradient related effects in arbitrary geometries with the lattice boltzmann methods need a trade off between the complexity of the scheme due to the loss of localness and the difficulties for directly applying link based approaches and the accuracy obtained a generalization of the momentum transfer boundary condition is presented in which the arbitrary location of the boundary is addressed with link wise interpolation used for dirichlet conditions and the macroscopic gradient is taken into account with a finite difference scheme this leads to a stable approach for arbitrary geometries that can be used to impose neumann and robin boundary conditions the proposal is validated for stress boundary conditions at walls two dimensional steady and unsteady configurations are used as test case partial slip flow between two infinite plates and the slip flow past a circular cylinder

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

analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice boltzmann bgk model in this paper we analytically solve the velocity of the lattice boltzmann bgk equation lbgk for several simple flows the analysis provides a framework to theoretically analyze various boundary conditions in particular the analysis is used to derive the slip velocities generated by various schemes for the nonslip boundary condition we find that the slip velocity is zero as long as f e 0 at boundaries no matter what combination of distributions is chosen the schemes proposed by nobleet al and by inamuroet al yield the correct zeroslip velocity while some other schemes such as the bounce back scheme and the equilibrium distribution scheme would inevitably generate a nonzero slip velocity the bounce back scheme with the wall located halfway between a flow node and a bounce back node is also studied for the simple flows considered and is shown to produce results of second order accuracy the momentum exchange at boundaries seems to be highly related to the slip velocity at boundaries to be specific the slip velocity is zero only when the momentum dissipated by boundaries is equal to the stress provided by fluids

error analysis and correction for lattice boltzmann simulated flow conductance in capillaries of different shapes and alignments we study the relative error in conductance calculations for simulated flow of a single component single phase fluid through a capillary in three dimensions by the lattice boltzmann lb method with bounce back boundary conditions the relative error with respect to analytical results for capillary cross sections of circular triangular and square shapes are calculated as a function of the cross section diameter a and for different alignment of the cross section relative to the underlying lattice grid it is shown when the shapes are not aligned perfectly to the lattice that the relative error decreases systematically with the size a as 1 a when a is evaluated by mapping the computed cross sectional area in terms of the enclosed number of grid points to the respective geometrical shapes concerned for perfectly aligned geometries viz the square capillary aligned to the lb lattice grid or rotated with its side along the diagonal of the lb grid the relative error decreases as 1 a 2 a simple method is suggested to locate the boundary wall depending on its orientation relative to the grid such that the exact conductance of the new shape matches the lb computed conductance

an onsager like relation for the lattice boltzmann method an onsager like relation is proposed as a new criterion for constructing and analyzing the lattice boltzmann lb method for lb models obeying the relation we analyze their linearized stability establish their diffusive limit and find new constraints for those with free parameters the new relation seems of fundamental importance for the lb method

truncation error analysis of lattice boltzmann methods a truncation error analysis is performed for models based on the lattice boltzmann lb equation this analysis involves two steps the recursive application of the lb equation and a taylor series expansion unlike previous analytical studies of lb methods the present work does not assume an asymptotic relationship between the temporal and spatial discretization parameters or between the probability distribution function f and its equilibrium distribution feq effective finite difference stencils are derived for both the distribution function and the primitive variables i e density and velocity the governing partial differential equations are also recovered the associated truncation errors are derived and the results are validated by numerical simulation of analytic flows analysis of the truncation errors elucidates the roles of the kinetic theory relaxation parameter and the discretization parameters x and t the effects of initial and boundary conditions are also addressed and are shown to significantly affect the overall accuracy of the method

chapman enskog analysis for finite volume formulation of lattice boltzmann equation the classical chapman enskog expansion is performed for the recently proposed finite volume formulation of lattice boltzmann equation lbe method d v patil k n lakshmisha finite volume tvd formulation of lattice boltzmann simulation on unstructured mesh j comput phys 228 2009 5262 5279 first a modified partial differential equation is derived from a numerical approximation of the discrete boltzmann equation then the multi scale small parameter expansion is followed to recover the continuity and the navier stokes ns equations with additional error terms the expression for apparent value of the kinematic viscosity is derived for finite volume formulation under certain assumptions the attenuation of a shear wave taylor green vortex flow and driven channel flow are studied to analyze the apparent viscosity relation

initial and boundary conditions for the lattice boltzmann method an alternative approach of implementing initial and boundary conditions for the lattice boltzmann method is presented the basic idea is to calculate the lattice boltzmann populations at a boundary node from the fluid variables that are specified at this node using the gradients of the fluid velocity the numerical performance of the lattice boltzmann method is tested on several problems with exact solutions and is also compared to an explicit finite difference projection method the discretization error of the lattice boltzmann method decreases quadratically with finer resolution both in space and in time the roundoff error of the lattice boltzmann method creates problems unless double precision arithmetic is used

smooth initialization of lattice boltzmann schemes lattice boltzmann methods are paradigmatic discrete evolutions with incomplete initial conditions this is due to the fact that the variables of the mesoscopic method outnumber the variables of the macroscopic problem to be solved in such situations most initializations which are compatible with the given macroscopic data lead to solutions with oscillatory or steep initial layers in order to reduce such initial effects we present a general approach to construct initial values which are compatible with the partial information available and which guarantee a smooth start of the evolution our smoothness condition prescribes the unknown initial values as the polynomial backward extrapolation of the values obtained from a few time steps specifically for constant and linear extrapolation we study the consistency stability and accuracy of the approach in the case of a lattice boltzmann method for one dimensional advection moreover the applicability of a simple iteration scheme as the solution method is investigated

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

new lifting relations for estimating lbm distribution functions from corresponding macroscopic quantities based on equilibrium and non equilibrium moments due to superior accuracy and stability of multiple relaxation time mrt collision operator over its single relaxation time srt counterpart new lifting relations are proposed here to construct single particle distribution functions for mrt lbm from macroscopic variables using these lifting relations a new hybrid fvm lb method is presented called finite type lb hybrid method which is consistent with mrt lbm in this new hybrid method single particle distribution functions in mrt lbm sub domain boundaries are computed using equilibrium and non equilibrium moments these moments are computed in navier stokes fvm sub domain boundaries using macroscopic variables and their derivatives the new method is validated by solving three benchmark problems i e two and three dimensional lid driven cavity flows and two dimensional unsteady flow around a squared section cylinder these problems are analyzed with pure fvm pure lbm and finite type lb hybrid method ftlbhm and the related results are compared with each other and with benchmark data these comparisons clearly demonstrate the accuracy of the present novel methodology for simulating steady unsteady flow fields in two and three dimensions new lifting relations are developed to construct a hybrid ns fvm lbm mrt method hybrid method is implemented to a 3 dimensional problem for the first time based on authors knowledge using new hybrid fvm lbm mrt method to simulate flow around complex geometries such as porous media

pressure condition for lattice boltzmann methods on domains with curved boundaries we propose a lattice boltzmann algorithm for an average pressure boundary condition at outlets in pipe flow systems the advantage of this boundary condition is that only the average pressure is used to recover the non trivial flow fields the asymptotic analysis shows that this algorithm works for general curved boundaries and renders a second order accurate velocity and a first order accurate pressure approximation of the incompressible navier stokes solution here we verify the accuracy by numerical simulations of a poiseuille flow and a less symmetric flow with non trivial pressure field in channels inclined with arbitrary angle and flows in a pipe with three outlets

the computation of strain rate tensor in multiple relaxation time lattice boltzmann model abstract the multiple relaxation time mrt lattice boltzmann lb model is an important class of lb model with lots of advantages over the traditional single relaxation time srt lb model generally the computation of strain rate tensor is crucial for the mrt lb simulations of some complex flows at present only two formulae are available to compute the strain rate tensor in the mrt lb model one is to compute the strain rate tensor using the non equilibrium parts of macroscopic moments yu formula the other is to compute the strain rate tensor using the non equilibrium parts of density distribution functions chai formula the mathematical expressions of these two formulae are so different that we do not know which formula to choose for computing the strain rate tensor in the mrt lb model to overcome this problem this paper presents a theoretical study of the relationship between chai and yu formulae the results show that the yu formula can be deduced from the chai formula although they have their own advantages and disadvantages in particular the yu formula is computationally more efficient while the chai formula is applicable to more lattice patterns of the mrt lb models furthermore the derivation of the yu formula in a particular lattice pattern from the chai formula is more convenient than that proposed by yu et al

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

direct assessment of lattice boltzmann hydrodynamics and boundary conditions for recirculating flows a hydrodynamic boundary condition is developed for lattice boltzmann hydrodynamics using a square orthogonal grid a constraint based on energy considerations is developed to provide closure for the equations which govern the particle distribution at the boundaries this boundary condition is applied to the two dimensional steady flow of an incompressible fluid behind a grid known as kovasznay flow the results are compared to those using alternate boundary conditions using the known exact solution the hydrodynamic boundary condition produces quadratic spatial convergence while alternate techniques fail to maintain this second order accuracy

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

direct and large eddy simulation of turbulent flows on composite multi resolution grids by the lattice boltzmann method in order to properly address the simulation of complex weakly compressible turbulent flows the lattice boltzmann method originally designed for uniform structured grids needs to be extended to composite multi domain grids displaying various levels of spatial resolution therefore physical conditions must be specified to determine the mapping of statistical information about the populations of moving particles at the interface between two domains of different resolutions quite simply in terms of the probability distributions of the underlying discrete velocity boltzmann equation namely the continuity of the mass density and fluid momentum is fulfilled by imposing the continuity of the equilibrium part of these distributions whereas the discontinuity of the rate of strain tensor is ensured by applying a spatial transformation to the collision term of the discrete velocity boltzmann equation the latter condition allows us to explicitly account for the subgrid scale modeling in the treatment of resolution changes test computations of a turbulent plane channel flow have been carried out the lattice boltzmann scheme relies on the standard d3q19 lattice in a cell vertex representation and uses the bgk approximation for the collision term a shear improved variant of the smagorinsky viscosity is used to account for possible subgrid scale dynamics in a quasi direct numerical simulation at re t 180 with two levels of grid resolution the results are found in excellent agreement with reference data obtained by a high resolution pseudo spectral simulation in a large eddy simulation les at re t 395 with three levels of grid resolution the results compare reasonably well with high resolution reference data the accuracy is improved in comparison with a standard finite volume les performed with the same subgrid scale viscosity and comparable grid resolution by combining the simplicity and physical relevance of the shear improved smagorinsky model and the computational efficiency of the lattice boltzmann scheme here extended to composite multi resolution grids we believe that our proposal offers a high potential for the simulation of complex turbulent flows

a curved no slip boundary condition for the lattice boltzmann method we present a generalization of the no slip boundary condition by latt et al j latt b chopard o malaspinas m deville a michler straight velocity boundaries in the lattice boltzmann method physical review e 77 5 2008 056703 from straight to curved geometries for the lattice boltzmann bhatnager gross krook method lbgk the boundary condition is based on a reconstruction of the populations from the density velocity and rate of strain for curved boundaries the reconstruction reduces the question of accuracy to a technical issue of interpolation we present a method of interpolation allowing a very accurate representation of the curved boundary the resulting boundary condition is verified for three different test cases taylor couette flow in between rotating cylinders laminar flow around a cylinder and flow past an impulsively started cylinder demonstrating its second order accuracy and low error constant the present boundary is stable for relaxation frequencies close to two

concept for a one dimensional discrete artificial boundary condition for the lattice boltzmann method this article deals with artificial boundaries which you encounter when a large spatial domain is confined to a smaller computational domain such an artificial boundary condition should not preferably interact with the fluid at all standard boundary conditions e g a pressure or velocity condition result in unphysical reflections so far existing artificial boundary conditions for the lattice boltzmann method lbm are transferred from macroscopic formulations in this work we propose novel discrete artificial boundary conditions abcs which are tailored on the lbm s mesoscopic level they are derived directly for the chosen lbm with the aim of higher accuracy we describe the idea of discrete abcs in a three velocity d1q3 model governing the navier stokes equations in one dimension numerical results finally demonstrate the superiority of our new boundary condition in terms of accuracy compared to previously used abcs

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

application of the lattice boltzmann method to transition in oscillatory channel flow in this study the applicability of the lattice boltzmann method to oscillatory channel flow with a zero mean velocity has been evaluated the model has been compared to exact analytical solutions in the laminar case re 100 where re is the reynolds number based on the stokes layer for the womersley parameter 1 31 in this regime there was good agreement between numerical and exact analytical solutions the model was then applied to study the primary instability of oscillatory channel flow with a zero mean velocity for these transitionary flows the parameters were varied in the range 400 re 1000 and 4 16 disturbances superimposed on the numerical solution triggered the two dimensional primary instability this phenomenon has not been numerically evaluated over the range of or re currently investigated the results are consistent with quasi steady linear stability theories and previous numerical investigations

lattice boltzmann method for one and two dimensional burgers equation abstract in this paper a new method higher order moment lattice boltzmann method for one and two dimensional burgers equation is proposed the lattice boltzmann models presented here are based on a series of lattice boltzmann equations in different time scales in order to achieve higher order accuracy we use seven and four moments of the equilibrium distribution function in one and two dimensional models respectively we find two kinds of strategy to seek equilibrium distribution functions for the two dimensional model with second order accuracy these two are equivalent when a scale factor k 2 3 lastly we provide a fine numerical result of a one dimensional burgers equation numerical examples show the method can be used to simulate one and two dimensional burgers equation

adaptive filtering for the lattice boltzmann method in this study a new selective filtering technique is proposed for the lattice boltzmann method this technique is based on an adaptive implementation of the selective filter coefficient the proposed model makes the latter coefficient dependent on the shear stress in order to restrict the use of the spatial filtering technique in sheared stress region where numerical instabilities may occur different parameters are tested on 2d test cases sensitive to numerical stability and on a 3d decaying taylorgreen vortex the results are compared to the classical static filtering technique and to the use of a standard subgrid scale model and give significant improvements in particular for low order filter consistent with the lbm stencil