an efficient closed form derivation of spatial green s function for finite dielectric structures using characteristic green s function rational function fitting method a uniform and closed form spatial green s function for finite dielectric structures is derived by using a combination of the characteristic green s function cgf and rational function fitting method rffm employing the concept of quasi leaky waves cgf rffm represents both of the discrete and continuous spectrum contributions efficiently by using the modified vectfit algorithm the method is examined for 2 d truncated dielectric slab while it can be implemented for 3 d structure straightforwardly an error of less than 0 2 is achieved compared with the direct numerical integration of the spectral integral the derived green s function is exact for separable structures while it is approximate for nonseparable structures like truncated dielectric substrates where the corner regions are replaced with fictitious materials to obtain more accurate results mode conversions due to the surface waves sws incident on the end facet are considered by employing the scattering matrix in the formulation for structures supporting several guided modes the main advantage of this method lies in its speed as well as accuracy excellent agreements with the rigorous method of moments mom are shown in several examples

direct rational function fitting method for accurate evaluation of sommerfeld integrals in stratified media the current work proposes a direct rational function fitting method employing cylindrical waves alone for the accurate evaluation of sommerfeld integrals for planar multilayered structures three are the key points of the effort 1 until now relative works require the extraction of the quasi static asymptotic terms and branch cut continuous wave contribution explicitly in the current one the explicit treatment of those terms is avoided the proposed methodology is based on the direct fitting of the spectrum of the green s function by rational functions thus it provides the spatial green s function solely in terms of cylindrical waves 2 the effectiveness robustness and accuracy improvement of the rational function fit rely upon the proper sampling of the spectrum this accurate fitting is possible because instead of avoiding large variations of the spectral kernel we introduce proper paths to include more variation and thus more spectrum information before we apply the modified vectfit algorithm 3 furthermore proper weighting of the vectfit is proposed in order to guide the algorithm in providing increased accuracy in specific desired areas of the horizontal distance between the source and observation points armed with the above the direct rational function fitting method provides accurate results both for the near and far field regions various examples among them the correct treatment of a two branch case are given that prove the excellent performance and robustness of the proposed approach

accurate approximation of green s functions in planar stratified media in terms of a finite sum of spherical and cylindrical waves a robust and computationally expedient methodology is presented for accurate closed form approximation of the green s functions used in the mixed potential integral equation statement of the electromagnetic boundary value problem in planar stratified media the proposed methodology is based on the fitting of the spectrum of the green s function after the extraction of the quasistatic part making use of rational functions the effectiveness and robustness of the proposed methodology rely upon the proper sampling of the spectrum in order to improve the accuracy of the rational function fit the resulting closed form approximation is in terms of both spherical and cylindrical waves thus high accuracy is obtained in the approximation of the green s function irrespective of the distance of the observation point from the source the methodology is validated through its application to the approximation of the green s function for a multi layered planar dielectric stack

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

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

an accurate derivation of spatial green s function for finite dielectric structures using characteristic green s function perfectly matched layer method a closed form spatial green s function for a truncated dielectric slab is derived by using a combination of the characteristic green s function cgf and perfectly matched layer pml method the original structure is terminated by pml that is backed by perfect electric conductor pec in semi infinite layer at the top and or bottom the eigenmodes of the closed structure by pml construct the continuous spectrum contribution of the original structure efficiently derived green s function is exact for separable finite structure while it is approximate for nonseparable one especially in the corners generalized scattering matrix gsm of truncating surface which contains possible conversions between all modes is computed with mode matching method it is demonstrated that by importing gsm in cgf formulation more exact results for nonseparable structures can be obtained the source and observation points dependence is analytically available in derived expression and allows very efficient computation and storage of the spatial green s function very close to the source where the large number of modes must be considered shank s transform is used to preserve the efficiency of the method the main advantage of the method lies in its accuracy and low dependency of the result to the pml parameters excellent agreements with the rigorous method of moments mom are shown in several examples

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

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

boundary stabilization of nonlinear vibrations of a flexible structure in a bounded domain in rn abstract we study a problem of boundary stabilization of the vibrations of elastic structure governed by the nonlinear integro differential equation u a 2 b u 2 d x u f in a bounded domain in r n with a smooth boundary under mixed boundary conditions to stabilize this system we apply a velocity feedback control only on a part of the boundary we prove that the solution of such system is stable subject to some restriction on the uncertain disturbing force f we also estimate the total energy of the system over any time interval 0 t with a tolerance level of the disturbances finally we establish the uniform decay of solution by a direct method with an explicit form of exponential energy decay estimate when this disturbing force f is insignificant

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

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

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

bounded input bounded output stability of a damped nonlinear string in this paper we prove that the displacement of a damped nonlinear string under bounded distributed forces is bounded the proof is achieved by showing that an energy like lyapunov function corresponding to the string is bounded

closed form green s function of a 2 d rectangular room closed form enough accurate green s function for wave propagation modeling in a rectangular 2 d room is presented using the characteristic green s function technique this green s function is first developed in an integral form then its spatial domain closed form is obtained using three fast methods in the first method the integral is computed by the stationary phase method in the second one the integral is computed analytically by expanding the integrand into a complex exponential series in the third method the integrand is approximated by a series of rational functions and the integral is computed using cauchy s residue theorem the results of these three methods are studied and compared in an example the results show that the methods are fast while preserving accuracy

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

stabilization of bernoulli euler beams by means of a pointwise feedback force we study the energy decay of a bernoulli euler beam which is subject to a pointwise feedback force we show that both uniform and nonuniform energy decay may occur the uniform or nonuniform decay depends on the boundary conditions in the case of nonuniform decay in the energy space we give explicit polynomial decay estimates valid for regular initial data our method consists of deducing the decay estimates from observability inequalities for the associated undamped problem via sharp trace regularity results

multilayered media green s functions in integral equation formulations a compact representation is given of the electric and magnetic type dyadic green s functions for plane stratified multilayered uniaxial media based on the transmission line network analog along the aids normal to the stratification furthermore mixed potential integral equations are derived within the framework of this transmission line formalism for arbitrarily shaped conducting or penetrable objects embedded in the multilayered medium the development emphasizes laterally unbounded environments but an extension to the case of a medium enclosed by a rectangular shield is also included

exponential stability of coupled beams with dissipative joints a frequency domain approach two examples of coupled euler bernoulli beams with a dissipative joint are considered the joint placements that lead to exponential stability for these systems are characterized the technique used shows input output stability of a related controlled observed system and then shows that in these examples input output stability implies exponential stability in the first example the energy dissipation arises from a discontinuity in the shear at the joint in the second example the energy dissipation arises from a discontinuity in the bending moment at the joint the analysis of this system involves a complete spectrum analysis of the zero dynamics of the associated controlled observed system

generalized pencil of function method for extracting poles of an em system from its transient response a generalized pencil of function gpof method is developed for extracting the poles of an electromagnetic system from its transient response the gpof method needs the solution of a generalized eigenvalue problem to find the poles subspace decomposition is also used to optimize the performance of the gpof method the gpof method has advantages over the prony method in both computation and noise sensitivity and approaches the cramer rao bound when the signal to noise ratio snr is above threshold an application of the gpof method to a thin wire target is presented

exact controllability stabilization and perturbations for distributed systems exact controllability is studied for distributed systems of hyperbolic type or for petrowsky systems like plate equations the control is a boundary control or a local distributed control exact controllability consists in trying to drive the system to rest in a given finite time the solution of the problems depends on the function spaces where the initial data are taken and also depends on the function space where the control can be chosen a systematic method named hum for hilbert uniqueness method is introduced as the terminology indicates it is based on uniqueness results classical or new and on hilbert spaces constructed in infinitely many ways by using uniqueness a number of applications are indicated having a general method for exact controllability implies having a general method for stabilization this leads to new and complicated nonlinear riccati s type pdes to be compared with direct methods when available in the last part of the paper we consider how all this behaves fo

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

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

exponential energy decay estimates for the solutions of n dimensional kirchhoff type wave equation here we study uniform exponential stabilization of the vibrations of kirchhoff type wave equation in a bounded domain in rn with a smooth boundary under mixed boundary conditions to stabilize the system we incorporate separately the passive viscous damping and the internal material damping of kelvin voigt type in the model explicit forms of exponential energy decay rates are obtained by a direct method for the solution of such boundary value problems

interior green s function solution for a thick and finite dielectric slab an interior green s function solution is presented for a two dimensional thick and finite dielectric slab in the present development the source and the field points are assumed to be inside the dielectric slab the result is composed of two parts the first part which has a discrete spectrum of eigenfunctions includes the surface wave multiple interactions and is obtained by using the generalized scattering matrix and method of moments the second part which is a closed form integral is obtained for a separable dielectric slab that is closely related to the finite slab the closed form integral is evaluated numerically and added to the surface wave solution the solution accounts for the mode conversions at the end caps which occur when surface waves are reflected and diffracted test cases show very good agreement with a finite element solver even when the source is near the end caps

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

exponential decay of energy of the euler bernoulli beam with locally distributed kelvin voigt damping in this paper we consider the longitudinal and transversal vibrations of the euler bernoulli beam with kelvin voigt damping distributed locally on any subinterval of the region occupied by the beam we prove that the semigroup associated with the equation for the transversal motion of the beam is exponentially stable although the semigroup associated with the equation for the longitudinal motion of the beam is not exponentially stable due to the locally distributed and unbounded nature of the damping we use a frequency domain method and combine a contradiction argument with the multiplier technique to carry out a special analysis for the resolvent we also show that the associated semigroups are not analytic

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

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

dynamic boundary control of a euler bernoulli beam a flexible beam clamped to a rigid base at one end and free at the other end is considered to stabilize the beam vibrations a dynamic boundary force control and a dynamic boundary torque control applied at the free end of the beam are proposed it is proved that with the proposed controls the beam vibrations decay exponentially the proof uses a lyapunov functional based on the energy functional of the system

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

stabilization of quasi linear vibrations of an inhomogeneous beam in this note we study the stabilization of a vibrating inhomogeneous beam under distributed disturbing force we prove that the amplitude of such vibration is bounded subject to some restriction on the uncertain disturbing force we also estimate the total energy of the system over time interval 0 t for any time t 0 together with a tolerance level of the disturbance finally we establish the uniform decay of solution with an explicit form of exponential energy decay estimate when the uncertain disturbances are insignificant

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

modeling stabilization and control of serially connected beams many flexible structures consist of a large number of components coupled end to end in the form of a chain in this paper we consider the simplest type of such structures which is formed by n seri

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

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