application of the multicomponent lattice boltzmann simulation method to oil water dispersions we study the propagation of acoustic fields in bounded two dimensional mono disperse oil water emulsions using a carefully modified and appropriately calibrated single relaxation time multicomponent lattice boltzmann equation simulation our model is a variant of an algorithm applying both interface forces based on macroscopic surface tensions and a kinematic condition for phase separation adapted to allow sonic speed variations between its oil and water components appropriate second order accurate acoustic boundary conditions are obtained from a node based lattice closure with local mass conservation and applicability for varying fluid viscosities data from an example simulation of a single oil drop in water interacting with a generated standing acoustic wave are presented and where appropriate compared with empirical theories and analogous calculations for a solid object

multiphase cascaded lattice boltzmann method to improve the stability of the lattice boltzmann method lbm at high reynolds number the cascaded lbm has recently been introduced as in the multiple relaxation time mrt method the cascaded lbm introduces additional relaxation times into the collision operator but does so in a co moving reference frame this has been shown to significantly increase stability at low viscosity in the single phase case here the cascaded lbm is further developed to include multiphase flow for this the force term is calculated by the interaction potential method and introduced into the collision operator via the exact difference method edm comparisons are made with the lattice bhatnagar gross krook lbgk method and an mrt implementation both the cascaded and mrt methods are shown to significantly reduce spurious velocities over the lbgk method for the particular case of the shan chen interparticle force term calculation with the edm the cascaded lbm is successfully combined with a multiphase method and shown to perform as well as the more established mrt method the cascaded lbm is found to be a considerably improved approach to the simulation of multiphase flow over the lbgk significantly increasing the stability range of both density ratio and reynolds number additionally the importance of including third order velocity terms in the equilibria of both the cascaded and mrt methods is discussed

homogenization of weakly coupled systems of hamilton jacobi equations with fast switching rates we consider homogenization for weakly coupled systems of hamilton jacobi equations with fast switching rates the fast switching rate terms force the solutions to converge to the same limit which is a solution of the effective equation we discover the appearance of the initial layers which appear naturally when we consider the systems with different initial data and analyze them rigorously in particular we obtain matched asymptotic solutions of the systems and the rate of convergence we also investigate properties of the effective hamiltonian of weakly coupled systems and show some examples which do not appear in the context of single equations

mesoscopic modeling of flow and dispersion phenomena in fractured solids the problem of hydrodynamic dispersion in porous media is considered and numerical predictions of the mixing degree in a single intersection are provided the flow field in the intersection and adjacent pores or fractures is calculated using a lattice boltzmann model for single phase flow a particle tracking scheme is used subsequently that monitors the migration of solute particles in the area of the intersection taking into account the local flow field and a brownian field mixing is quantified in terms of the probability of solute transfer across the junction into the opposite fracture to circumvent the problem of large computational times for cases of fast flow compared to diffusion a lattice boltzmann advection diffusion model is used that offers significant savings on computational time without sacrificing accuracy it is shown that the solute dispersion in a fracture network is a strong function of the reynolds number even if the peclet number remains constant due to the extensive recirculation areas that may develop in regions close to the junction

effects of density and force discretizations on spurious velocities in lattice boltzmann equation for two phase flows spurious current emerging in the vicinity of phase interfaces is a well known disadvantage of the lattice boltzmann equation lbe for two phase flows previous analysis shows that this unphysical phenomenon comes from the force imbalance at discrete level inherited in lbe guo et al 2011 phys rev e 83 036707 based on the analysis of the lbe free of checkerboard effects in this work we further show that the force imbalance is caused by the different discretization stencils the implicit one from the streaming process and the explicit one from the discretization of the force term particularly the total contribution includes two parts one from the difference between the intrinsically discretized density or ideal gas pressure gradient and the explicit ones in the force term and the other from the explicit discretized chemical potential gradients in the intrinsically discretized force term the former contribution is a special feature of lbe which was not realized previously

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

discrete lattice effects on the forcing term in the lattice boltzmann method we show that discrete lattice effects must be considered in the introduction of a force into the lattice boltzmann equation a representation of the forcing term is then proposed with the representation the navier stokes equation is derived from the lattice boltzmann equation through the chapman enskog expansion several other existing force treatments are also examined

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

an efficient lattice boltzmann multiphase model for 3d flows with large density ratios at high reynolds numbers we report on the development implementation and validation of a new lattice boltzmann method lbm for the numerical simulation of three dimensional multiphase flows here with only two components with both high density ratio and high reynolds number this method is based in part on but aims at achieving a higher computational efficiency than inamuro et al s model inamuro et al 2004 here we use a lbm to solve both a pressureless navier stokes equation in which the implementation of viscous terms is improved and a pressure poisson equation using different distribution functions and a d3q19 lattice scheme additionally we propose a new diffusive interface capturing method based on the cahn hilliard equation which is also solved with a lbm to achieve maximum efficiency the entire model is implemented and solved on a heavily parallel gpgpu co processor the proposed algorithm is applied to several test cases such as a splashing droplet a rising bubble and a braking ocean wave in all cases numerical results are found to agree very well with reference data and or to converge with the discretization

steady state convergence acceleration of the generalized lattice boltzmann equation with forcing term through preconditioning several applications exist in which lattice boltzmann methods lbm are used to compute stationary states of fluid motions particularly those driven or modulated by external forces standard lbm being explicit time marching in nature requires a long time to attain steady state convergence particularly at low mach numbers due to the disparity in characteristic speeds of propagation of different quantities in this paper we present a preconditioned generalized lattice boltzmann equation glbe with forcing term to accelerate steady state convergence to flows driven by external forces the use of multiple relaxation times in the glbe allows enhancement of the numerical stability particular focus is given in preconditioning external forces which can be spatially and temporally dependent in particular correct forms of moment projections of source forcing terms are derived such that they recover preconditioned navier stokes equations with non uniform external forces as an illustration we solve an extended system with a preconditioned lattice kinetic equation for magnetic induction field at low magnetic prandtl numbers which imposes lorentz forces on the flow of conducting fluids computational studies particularly in three dimensions for canonical problems show that the number of time steps needed to reach steady state is reduced by orders of magnitude with preconditioning in addition the preconditioning approach resulted in significantly improved stability characteristics when compared with the corresponding single relaxation time formulation

nonequilibrium scheme for computing the flux of the convection diffusion equation in the framework of the lattice boltzmann method in this paper we propose a local nonequilibrium scheme for computing the flux of the convection diffusion equation with a source term in the framework of the multiple relaxation time mrt lattice boltzmann method lbm both the chapman enskog analysis and the numerical results show that at the diffusive scaling the present nonequilibrium scheme has a second order convergence rate in space a comparison between the nonequilibriumschemeandtheconventionalsecond ordercentral differenceschemeindicatesthat althoughboth schemes have a second order convergence rate in space the present nonequilibrium scheme is more accurate than thecentral differencescheme inaddition thefluxcomputationrenderedbythepresentschemealsopreservesthe parallel computation feature of the lbm making the scheme more efficient than conventional finite difference schemes in the study of large scale problems finally a comparison between the single relaxation time model and the mrt model is also conducted and the results show that the mrt model is more accurate than the single relaxation time model both in solving the convection diffusion equation and in computing the flux

a lattice boltzmann method for axisymmetric multicomponent flows with high viscosity ratio a color gradient lattice boltzmann method lbm is proposed to simulate axisymmetric multicomponent flows this method uses a collision operator that is a combination of three separate parts namely single component collision operator perturbation operator and recoloring operator a source term is added into the single component collision operator such that in each single component region the axisymmetric continuity and momentum equations can be exactly recovered the interfacial tension effect is realized by the perturbation operator in which an interfacial force of axisymmetric form is derived using the concept of continuum surface force a recoloring operator proposed by latva kokko and rothman is extended to the axisymmetric case for phase segregation and maintenance of the interface to enhance the method s numerical stability for handling binary fluids with high viscosity ratio a multiple relaxation time model is used for the collision operator several numerical examples including static droplet test oscillation of a viscous droplet and breakup of a liquid thread are presented to test the capability and accuracy of the proposed color gradient lbm it is found that the present method is able to accurately capture the phase interface and produce low spurious velocities also the lbm results are all in good agreement with the analytical solutions and or available experimental data for a very broad range of viscosity ratios a color gradient lbm is developed for immiscible axisymmetric multiphase flows the method consists of three separate operators in which axisymmetric effects are considered the method is demonstrated to be accurate for a very wide range of viscosity ratios viscosity ratio is found to affect significantly growth of rayleigh instability but have negligible effect on droplet size

effect of the forcing term in the multiple relaxation time lattice boltzmann equation on the shear stress or the strain rate tensor in this work the effect of the forcing term or external force in the multiple relaxation time lattice boltzmann equation mrtlbe on the shear stress or the strain rate tensor is studied theoretically and numerically through a chapman enskog analysis and numerical simulations we show that the shear stress or the strain rate tensor derived from the mrtlbe is second order accurate in space we then examine the influence of the forcing term on the shear stress or the strain rate tensor and demonstrate that the forcing term effect must be included when the shear stress or the strain rate tensor is computed with the nonequilibrium part of the distribution function

accuracy of non newtonian lattice boltzmann simulations this work deals with the accuracy of non newtonian lattice boltzmann simulations previous work for newtonian fluids indicate that depending on the numerical value of the dimensionless collision frequency additional artificial viscosity is introduced which negatively influences the accuracy since the non newtonian fluid behavior is incorporated through appropriate modeling of the dimensionless collision frequency a dependent error e is introduced and its influence on the overall error is investigated here simulations with the srt and the mrt model are carried out for power law fluids in order to numerically investigate the accuracy of non newtonian lattice boltzmann simulations a goal of this accuracy analysis is to derive a recommendation for an optimal choice of the time step size and the simulation mach number respectively for the non newtonian case an error estimate for e in the form of a functional is derived on the basis of a series expansion of the lattice boltzmann equation this functional can be solved analytically for the case of the hagen poiseuille channel flow of non newtonian fluids with the help of the error functional the prediction of the global error minimum of the velocity field is excellent in regions where the e error is the dominant source of error with an optimal simulation mach number the simulation is about one order of magnitude more accurate additionally for both collision models a detailed study of the convergence behavior of the method in the non newtonian case is conducted the results show that the simulation mach number has a major impact on the convergence rate and second order accuracy is not preserved for every choice of the simulation mach number

an alternative implementation of the kinetic theory based axisymmetric lattice boltzmann model abstract the semi implicit centered scheme as an approximated implementation of the trapezium rule based scheme has proved to be capable of avoiding the discrete lattice effects in our recent forcing scheme analysis for the axisymmetric lb method and is applied here for an alternative implementation of the kinetic theory based axisymmetric model by guo et al in particular the external force terms and the first order part of the source terms accounting for the axisymmetric effect are discretized with the semi implicit centered scheme while the rest are represented with the trapezium rule the proposed axisymmetric lb scheme has the advantage of simpler calculations of the macroscopic variables since the zeroth and the first order moments of the distribution function are independent of the complicated source terms chapman enskog analysis in the appendix demonstrates that axisymmetric navier stokes n s equations are recovered from the proposed model and the error terms caused by the semi implicit centered scheme do not affect the overall accuracy of the present model moreover the accuracy and applicability of the proposed axisymmetric lb model are verified by the adopted numerical tests and the complicated macroscopic variables computations in the guo et al model and its derivative models are avoided by the present model

study of the 1d lattice boltzmann shallow water equation and its coupling to build a canal network the d1q3 lattice boltzmann lb shallow water equation is analyzed in detail and compared with other numerical schemes analytical results are derived and used to discuss the accuracy and stability of the model we show how such d1q3 lb models for canal reaches may be easily coupled with various hydraulic interconnection structures to build models of complex irrigation networks

an interpretation and derivation of the lattice boltzmann method using strang splitting the lattice boltzmann space time discretisation as usually derived from integration along characteristics is shown to correspond to a strang splitting between decoupled streaming and collision steps strang splitting offers a second order accurate approximation to evolution under the combination of two non commuting operators here identified with the streaming and collision terms in the discrete boltzmann partial differential equation strang splitting achieves second order accuracy through a symmetric decomposition in which one operator is applied twice for half timesteps and the other operator is applied once for a full timestep we show that a natural definition of a half timestep of collisions leads to the same change of variables that was previously introduced using different reasoning to obtain a second order accurate and explicit scheme from an integration of the discrete boltzmann equation along characteristics this approach extends easily to include general matrix collision operators and also body forces finally we show that the validity of the lattice boltzmann discretisation for grid scale reynolds numbers larger than unity depends crucially on the use of a crank nicolson approximation to discretise the collision operator replacing this approximation with the readily available exact solution for collisions uncoupled from streaming leads to a scheme that becomes much too diffusive due to the splitting error unless the grid scale reynolds number remains well below unity

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

semidefinite programming relaxations for graph coloring and maximal clique problems the semidefinite programming formulation of the lovasz theta number does not only give one of the best polynomial simultaneous bounds on the chromatic number g or the clique number g of a graph but also leads to heuristics for graph coloring and extracting large cliques this semidefinite programming formulation can be tightened toward either g or g by adding several types of cutting planes we explore several such strengthenings and show that some of them can be computed with the same effort as the theta number we also investigate computational simplifications for graphs with rich automorphism groups

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

total enthalpy based lattice boltzmann method with adaptive mesh refinement for solid liquid phase change a total enthalpy based lattice boltzmann lb method with adaptive mesh refinement amr is developed in this paper to efficiently simulate solid liquid phase change problem where variables vary significantly near the phase interface and thus finer grid is required for the total enthalpy based lb method the velocity field is solved by an incompressible lb model with multiple relaxation time mrt collision scheme and the temperature field is solved by a total enthalpy based mrt lb model with the phase interface effects considered and the deviation term eliminated with a kinetic assumption that the density distribution function for solid phase is at equilibrium state a volumetric lb scheme is proposed to accurately realize the nonslip velocity condition on the diffusive phase interface and in the solid phase as compared with the previous schemes this scheme can avoid nonphysical flow in the solid phase as for the amr approach it is developed based on multiblock grids an indicator function is introduced to control the adaptive generation of multiblock grids which can guarantee the existence of overlap area between adjacent blocks for information exchange since mrt collision schemes are used the information exchange is directly carried out in the moment space numerical tests are firstly performed to validate the strict satisfaction of the nonslip velocity condition and then melting problems in a square cavity with different prandtl numbers and rayleigh numbers are simulated which demonstrate that the present method can handle solid liquid phase change problem with high efficiency and accuracy

preconditioned lattice boltzmann method for steady flows in this paper we propose a preconditioned lattice boltzmann lb method for steady incompressible flows for steady flows the macroscopic equations derived from this lb model are equivalent to those from the standard lb model but with an improved eigenvalue system the proposed model can be viewed as an explicit solver for preconditioned compressible navier stokes equations linear stability analysis is performed and the results show that the stability of the model is the same as that of the standard lb model for low mach numbers the proposed model retains the structure of the standard lb model and hence possesses all the advantages numerical tests show that the convergence rate can be enhanced as much as an order of magnitude compared to the standard lattice boltzmann method the accuracy of the solutions is improved as well

an arbitrary lagrangian eulerian approach for the simulation of immersed moving solids with lattice boltzmann method the flow structure interactions streaming from the motion of an immersed solid body are investigated through an arbitrary lagrangian eulerian ale approach applied to the lattice boltzmann method lbm the method is based on the use of a moving grid to describe the flow around the solid body while the physical domain is resolved by the use of an eulerian frame fixed grid the moving grid displacements follows the same moving law of the body and its shape does not change during the simulation the communication between the moving grid and the fixed grid is performed at the beginning of each time step through interpolation the ale lbm approach has been derived from the discretized boltzmann equation by a chapman enskog expansion procedure the equivalence of the proposed method with the navier stokes equations for a weakly compressible athermal flow being recovered numerical simulations of academical test cases have been performed in order to assess the method and to investigate the sensitivity of the error to the simulation parameters three different test cases have been considered in order to perform a robust assessment of the ale lbm approach more specifically the uniform flow the poiseuille flow and the plane wave test cases have been studied and the limits of application of the approach have been defined and discussed finally the case of a rotating two dimensional square cylinder immersed in a poiseuille flow re 80 has been numerically investigated the results confirm that the ale lbm approach is able to correctly represent the physical flow features and in particular the transition zone between the two grids used is smooth and continuous a sign that the error due to the interpolation process is bounded and does not diverge in time

multirange multi relaxation time shan chen model with extended equilibrium the work presents simulations with the multirange shan chen model developed by sbragaglia et al 2007 18 which improved the shan chen model for the proper surface tension term also by introducing the matrix collision operator and extended equilibrium density distribution function the density ratio is increased from 100 to 160 the multi relaxation time mrt method attracted the attention of researchers due to several advantages such as better stability simulations with prandtl number different from unity and possibilities to improve the accuracy of the scheme compared with bgk single time relaxation model our recent results have shown that the combination of mrt methods with multiphase flow models can improve the achievable gas liquid density ratio