stability analysis of lattice boltzmann methods the lattice boltzmann equation describes the evolution of the velocity distribution function on a lattice in a manner that macroscopic fluid dynamical behavior is recovered although the equation is a derivative of lattice gas automata it may be interpreted as a lagrangian finite difference method for the numerical simulation of the discrete velocity boltzmann equation that makes use of a bgk collision operator as a result it is not surprising that numerical instability of lattice boltzmann methods have been frequently encountered by researchers we present an analysis of the stability of perturbations of the particle populations linearized about equilibrium values corresponding to a constant density uniform mean flow the linear stability depends on the following parameters the distribution of the mass at a site between the different discrete speeds the bgk relaxation time the mean velocity and the wavenumber of the perturbations this parameter space is too large to compute the complete stability characteristics we report some stability results for a subset of the parameter space for a 7 velocity hexagonal lattice a 9 velocity square lattice and a 15 velocity cubic lattice results common to all three lattices are 1 the bgk relaxation time must be greater than 12 corresponding to positive shear viscosity 2 there exists a maximum stable mean velocity for fixed values of the other parameters and 3 as is increased from 12 the maximum stable velocity increases monotonically until some fixed velocity is reached which does not change for larger

entropic lattice boltzmann representations required to recover navier stokes flows there are two disparate formulations of the entropic lattice boltzmann scheme one of these theories revolves around the analog of the discrete boltzmann h function of standard extensive statistical mechanics while the other revolves around the nonextensive tsallis entropy it is shown here that it is the nonenforcement of the pressure tensor moment constraints that lead to extremizations of entropy resulting in tsallis like forms however with the imposition of the pressure tensor moment constraint as is fundamentally necessary for the recovery of the navier stokes equations it is proved that the entropy function must be of the discrete boltzmann form three dimensional simulations are performed which illustrate some of the differences between standard lattice boltzmann and entropic lattice boltzmann schemes as well as the role played by the number of phase space velocities used in the discretization

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

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

on the congruence subgroup problem for integral group rings abstract let g be a finite group z g the integral group ring of g and u z g the group of units of z g the congruence subgroup problem for u z g is the problem of deciding if every subgroup of finite index of u z g contains a congruence subgroup i e the kernel of the natural homomorphism u z g u z g m z g for some positive integer m the congruence kernel of u z g is the kernel of the natural map from the completion of u z g with respect to the profinite topology to the completion with respect to the topology defined by the congruence subgroups the congruence subgroup problem has a positive solution if and only if the congruence kernel is trivial we obtain an approximation to the problem of classifying the finite groups for which the congruence kernel of u z g is finite more precisely we obtain a list l formed by three families of finite groups and 19 additional groups such that if the congruence kernel of u z g is infinite then g has an epimorphic image isomorphic to one of the groups of l regarding the converse of this statement we at least know that if one of the 19 additional groups in l is isomorphic to an epimorphic image of g then the congruence kernel of u z g is infinite however to decide for the finiteness of the congruence kernel in case g has an epimorphic image isomorphic to one of the groups in the three families of l one needs to know if the congruence kernel of the group of units of an order in some specific division algebras is finite and this seems a difficult problem

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

toward advanced subgrid models for lattice boltzmann based large eddy simulation theoretical formulations this paper addresses the issue of developing advanced subgrid model for large eddy simulations les of turbulent flows based on lattice boltzmann methods lbm most of already existing subgrid closures used in les lbm are straightforward extensions of the most crude model developed within the navier stokes equations namely the smagorinsky eddy viscosity model in a first part it is shown how to obtain an improved eddy viscosity subgrid model for lbm the original implementation of the inertial range consistent smagorinsky model proposed by dong and sagaut for the d3q19 scheme is used as an illustration in a second step an original extension of the approximate deconvolution method proposed by adams and stolz for navier stokes simulation is proposed this new lbm les approach does not rely on the eddy viscosity concept and is written directly within the lbm framework it is shown that it can be implemented thanks to a trivial modification of the existing lbm solvers for direct numerical simulation

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

optimal stability of advection diffusion lattice boltzmann models with two relaxation times for positive negative equilibrium despite the growing popularity of lattice boltzmann schemes for describing multi dimensional flow and transport governed by non linear anisotropic advection diffusion equations there are very few analytical results on their stability even for the isotropic linear equation in this paper the optimal two relaxation time otrt model is defined along with necessary and sufficient easy to use von neumann stability conditions for a very general anisotropic advection diffusion equilibrium in one to three dimensions with or without numerical diffusion quite remarkably the otrt stability bounds are the same for any peclet number and they are defined by the adjustable equilibrium parameters such optimal stability is reached owing to the free kinetic relaxation parameter furthermore the sufficient stability bounds tolerate negative equilibrium functions the distribution divided by the local mass often labeled as unphysical we prove that the non negativity condition is i a sufficient stability condition of the trt model with any eigenvalues for the pure diffusion equation ii a sufficient stability condition of its otrt and bgk srt sub classes for any linear anisotropic advection diffusion equation and iii unnecessarily more restrictive for any peclet number than the optimal sufficient conditions adequate choices of the two relaxation rates and the free tunable equilibrium parameters make the otrt sub class more efficient than the bgk one at least in the advection dominant regime and allow larger time steps than known criteria of the forward time central finite difference schemes ftcs mftcs for both advection and diffusion dominant regimes

lattice boltzmann model for the compressible navier stokes equations with flexible specific heat ratio we have developed a lattice boltzmann model for the compressible navier stokes equations with a flexible specific heat ratio several numerical results are presented and they agree well with the corresponding solutions of the navier stokes equations in addition an explicit finite difference scheme is proposed for the numerical calculation that can make a stable calculation with a large courant number

link wise artificial compressibility method the artificial compressibility method acm for the incompressible navier stokes equations is link wise reformulated referred to as lw acm by a finite set of discrete directions links on a regular cartesian mesh in analogy with the lattice boltzmann method lbm the main advantage is the possibility of exploiting well established technologies originally developed for lbm and classical computational fluid dynamics with special emphasis on finite differences at least in the present paper at the cost of minor changes for instance wall boundaries not aligned with the background cartesian mesh can be taken into account by tracing the intersections of each link with the wall analogously to lbm technology lw acm requires no high order moments beyond hydrodynamics often referred to as ghost moments and no kinetic expansion like finite difference schemes only standard taylor expansion is needed for analyzing consistency preliminary efforts towards optimal implementations have shown that lw acm is capable of similar computational speed as optimized bgk lbm in addition the memory demand is significantly smaller than bgk lbm importantly with an efficient implementation this algorithm may be among the few which are compute bound and not memory bound two and three dimensional benchmarks are investigated and an extensive comparative study between the present approach and state of the art methods from the literature is carried out numerical evidences suggest that lw acm represents an excellent alternative in terms of simplicity stability and accuracy

nonorthogonal central moments based lattice boltzmann scheme in three dimensions we present an alternative three dimensional lattice boltzmann collision operator consisting of a nonorthogonal basis of central moments our formulation is characterized by an intelligible derivation with a relatively simple and quite general implementation it is successfully validated against several established well consolidated well defined benchmark problems showing excellent properties in terms of accuracy and convergence if compared to the adoption of the classical bhatnagar gross krook operator our model possesses superior stability

on a superconvergent lattice boltzmann boundary scheme in a seminal paper 20 ginzburg and adler 1994 analyzed the bounce back boundary conditions for the lattice boltzmann scheme and showed that it could be made exact to second order for the poiseuille flow if some expressions depending upon the parameters of the method were satisfied thus defining so called magic parameters using the taylor expansion method that one of us developed we analyze a series of simple situations 1d and 2d for diffusion and for linear fluid problems using bounce back and anti bounce back numerical boundary conditions the result is that magic parameters depend upon the detailed choice of the moments and of their equilibrium values they may also depend upon the way the flow is driven

using g algebras for schur index computation abstract conditions for the existence of a bijective character correspondence that preserves schur indices are given based on the theory of central simple g algebras over fields of characteristic 0 it is then shown how this applies to schur index computation in the case of finite solvable groups

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

lattice boltzmann method with selective viscosity filter for high reynolds number flows the lattice boltzmann method suffers from numerical instabilities that can induce local blowup of the computation the von neumann stability analysis applied to the lbe bgk and lbe mrt models shows that numerical instabilities occur in the high wavenumber range and are due to the interplay between acoustic modes and some other modes as it is done in the lbe mrt model an increase of the bulk viscosity is an efficient way of damping spurious oscillations however this stabilization method induces an over damping of acoustic waves some selective spatial filters can be used in order to eliminate the spurious small spatial scales without affecting the large scale physical modes three different lattice boltzmann algorithms based on filtering step are proposed the fully filtered lbe the lbe with filtered macroscopic quantities and the lbe with filtered collision operator the behavior of several explicit filter stencils is studied in the fourier space for a given filter stencil the filtered collision operator approach leads to the highest cut off wavenumber in this case the theoretical wavenumber dependent viscosity is n k c s 2 t email protected k 1 2 where f k is the filter shape and s the filter strength under resolved simulations high reynolds number are performed on the case of the doubly periodic shear layers the performance of the three filtered lbe is found to be the same as the mrt model for stability control propagation of acoustic plane waves is also simulated with the three filtering algorithms the measured dissipation of acoustic wave compares well with the theoretical results

on trigonal non gorenstein curves with zero maroni invariant abstract by means of canonical models we answer some questions on trigonal non gorenstein curves with zero maroni invariant the number of non gorenstein points the kind of such singularities possible canonical models uniqueness and number of base points of a g 1 3 on the curve

comparison between lattice boltzmann method and navier stokes high order schemes for computational aeroacoustics computational aeroacoustic caa simulation requires accurate schemes to capture the dynamics of acoustic fluctuations which are weak compared with aerodynamic ones in this paper two kinds of schemes are studied and compared the classical approach based on high order schemes for navier stokes like equations and the lattice boltzmann method the reference macroscopic equations are the 3d isothermal and compressible navier stokes equations a von neumann analysis of these linearized equations is carried out to obtain exact plane wave solutions three physical modes are recovered and the corresponding theoretical dispersion relations are obtained then the same analysis is made on the space and time discretization of the navier stokes equations with the classical high order schemes to quantify the influence of both space and time discretization on the exact solutions different orders of discretization are considered with and without a uniform mean flow three different lattice boltzmann models are then presented and studied with the von neumann analysis the theoretical dispersion relations of these models are obtained and the error terms of the model are identified and studied it is shown that the dispersion error in the lattice boltzmann models is only due to the space and time discretization and that the continuous discrete velocity boltzmann equation yield the same exact dispersion as the navier stokes equations finally dispersion and dissipation errors of the different kind of schemes are quantitatively compared it is found that the lattice boltzmann method is less dissipative than high order schemes and less dispersive than a second order scheme in space with a 3 step runge kutta scheme in time the number of floating point operations at a given error level associated with these two kinds of schemes are then compared

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

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

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

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

grid refinement for aeroacoustics in the lattice boltzmann method a directional splitting approach this study focuses on grid refinement techniques for the direct simulation of aeroacoustics when using weakly compressible lattice boltzmann models such as the d3q19 athermal velocity set when it comes to direct noise computation very small errors on the density or pressure field may have great negative consequences even strong acoustic density fluctuations have indeed a clearly lower amplitude than the hydrodynamic ones this work deals with such very weak spurious fluctuations that emerge when a vortical structure crosses a refinement interface which may contaminate the resulting aeroacoustic field we show through an extensive literature review that within the framework described above this issue has never been addressed before to tackle this problem we develop an alternative algorithm and compare its behavior to a classical one which fits our in house vertex centered data structure our main idea relies on a directional splitting of the continuous discrete velocity boltzmann equation followed by an integration over specific characteristics this method can be seen as a specific coupling between finite difference and lattice boltzmann locally on the interface between the two grids the method is assessed considering two cases an acoustic pulse and a convected vortex we show how very small errors on the density field arise and propagate throughout the domain when a vortical flow crosses the refinement interface we also show that an increased free stream mach number but still within the weakly compressible regime strongly deteriorates the situation although the magnitude of the errors may remain negligible for purely aerodynamic studies a drastically reduced level of error for the near field spurious noise is obtained with our approach especially for under resolved simulations a situation that is crucial for industrial applications thus the vortex case is proved useful for aeroacoustic validations of any grid refinement algorithm

coarse and fine grid numerical behavior of mrt trt lattice boltzmann schemes in regular and random sphere packings we analyze the intrinsic impact of free tunable combinations of the relaxation rates controlling viscosity independent accuracy of the multiple relaxation times mrt lattice boltzmann models preserving all mrt degrees of freedom we formulate the parametrization conditions which enable the mrt schemes to provide viscosity independent truncation errors for steady state solutions and support them with the second and third order accurate linear and parabolic respectively boundary schemes the parabolic schemes demonstrate the advanced accuracy with weak dependency on the relaxation rates as confirmed by the simulations with the d3q15 model in three regular arrays sc bcc fcc of touching spheres yet the low order bounce back boundary rule remains appealing for pore scale simulations where the precise distance to the boundaries is undetermined however the effective accuracy of the bounce back crucially depends on the free tunable combinations of the relaxation rates we find that the combinations of the kinematic viscosity rate with the available ghost antisymmetric collision mode rates mainly impact the accuracy of the bounce back scheme as the first step we reduce them to the one combination presented by so called magic parameter in the frame of the two relaxation times trt model and study its impact on the accuracy of the drag force permeability computations with the d3q19 velocity set in two different dense random packings of 8000 spheres each we also run the simulations in the regular bcc and fcc packings of the same porosity for the broad range of the discretization resolutions ranging from 5 to 750 lattice nodes per sphere diameter a special attention is given to the discretization procedure resulting in significantly reduced scatter of the data obtained at low resolutions the results reveal the identical dependency versus the discretization resolution in all four packings regular and random while very small values overestimate the drag measurements several fold on the coarse grids 1 may overestimate the permeability at the same extent in low resolution region we provide practical guidelines extending previously known solutions for the straight diagonal poiseuille flow analysis of the high resolution region reveals the collapse of the solutions obtained with all the considered values with the average rate of 1 3 followed by their common smooth first order convergence with the rate of 1 0 as the best towards the reference solutions provided by the parabolic schemes high quality power law fits estimate that the bounce back would reach their accuracy obtained at about 200 nodes per sphere for two order magnitude higher grid resolution the parametrization conditions enable the mrt lbe to provide viscosity independent truncation spatial errors these schemes are supported with the high order accurate boundary conditions confirmed in touching arrays of spheres the effect of free relaxation rates on drag force computations is examined for bounce back and high order conditions random and regular packings demonstrate identical numerical errors for various relaxation rates and resolutions for low resolution we provide practical guidelines while high resolutions revealed first order convergence to reference drag

group algebras of kleinian type and groups of units the algebras of kleinian type are finite dimensional semisimple rational algebras a such that the group of units of an order in a is commensurable with a direct product of kleinian groups we classify the schur algebras of kleinian type and the group algebras of kleinian type as an application we characterize the group rings rg with r an order in a number field and g a finite group such that rgis virtually a direct product of free by free groups the study of kleinian groups goes back to the works of poincar poi and bianchi bia and it has been an active field of research ever since in the last decades it is strongly related to the geometrization program of thurston for the classification of 3 manifolds egm mr mas thu the use of the methods of kleinian groups to the study of the groups of units of group rings was started in prr and led to the notion of algebras of kleinian type and finite groups of kleinian type let k be a number field a a central simple k algebra and r a z order in a let r 1 denote the group of units of r of reduced norm 1 every embedding k c induces an embedding a md c where d is the degree of a furthermore r 1 sld c we say that a is of kleinian type if either a k or a is a quaternion algebra over k and r 1 is a discrete subgroup of sl2 c for some embeddingof k in c more generally an algebra of kleinian type prr is by definition a direct sum of simple algebras of kleinian type a finite group g is of kleinian type if and only if the rational group algebra qg is of kleinian type the finite groups of kleinian type have been classified in jprrz where it has been also proved that a finite group g is of kleinian type if and only if the group of units zg of its integral group ring zg is commensurable with a direct product of free by free groups recently alan reid asked us in a private communication about the consequences of replacing the ring of rational integers by another ring of integers this leads to the following two problems problem 1 classify the group algebras of kleinian type of finite groups over number fields problem 2 given a group algebra of kleinian type kg describe the structure of the group of units of the group ring rg for r an order in k

sensitivity analysis and determination of free relaxation parameters for the weakly compressible mrt lbm schemes lattice boltzmann methods lbms are very efficient for computational fluid dynamics and for capturing the dynamics of weak acoustic fluctuations it is known that multi relaxation time lattice boltzmann method mrt lbm appears as a very robust scheme with high precision there exist several free relaxation parameters in the mrt lbm although these parameters have been tuned via linear analysis the sensitivity analysis of these parameters and other related parameters is still not sufficient for describing the behavior of the dispersion and dissipation relations of the mrt lbm previous researches have shown that the bulk dissipation in the mrt lbm induces a significant over damping of acoustic disturbances this indicates that the classical mrt lbm is not best suited to recover the correct behavior of pressure fluctuations in wave number space the first second order sensitivity analyses of matrix eigenvalues are used to address the sensitivity of the wavenumber magnitudes to the dispersion dissipation relations by the first order sensitivity analysis the numerical behaviors of the group velocity of the mrt lbm are first obtained afterwards the distribution sensitivities of the matrix eigenvalues corresponding to the linearized form of the mrt lbm are investigated in the complex plane based on the sensitivity analysis and an effective algorithm of recovering linearized navier stokes equations l nses from linearized mrt lbm l mrt lbm we propose some simplified optimization strategies to determine the free relaxation parameters of the mrt lbm meanwhile the dispersion and dissipation relations of the optimal mrt lbm are quantitatively compared with the exact dispersion and dissipation relations at last some numerical validations on classical acoustic benchmark problems are shown to assess the new optimal mrt lbm

lattice boltzmann equation linear stability analysis thermal and athermal models although several thermal lattice boltzmann models have been proposed this method has not yet been shown to be able to describe nonisothermal fully compressible flows in a satisfactory manner mostly due to the presence of important deviations from the advection diffusion macroscopic equations and also due to numerical instabilities in this context this paper presents a linear stability analysis for some lattice boltzmann models that were recently derived as discrete forms of the continuous boltzmann equation p c philippi l a hegele jr l o e dos santos and r surmas phys rev e 63 056702 2006 in order to investigate the sources of instability and to find for each model the upper and lower limits for the macroscopic variables between which it is possible to ensure a stable behavior the results for two dimensional 2d lattices with 9 17 25 and 37 velocities indicate that increasing the order of approximation of the lattice boltzmann equation enhances stability results are also presented for an athermal 2d nine velocity model the accuracy of which has been improved with respect to the standard d2q9 model by adding third order terms in the lattice boltzmann equation

towards a physical interpretation of the entropic lattice boltzmann method reference lin article 2009 005doi 10 1103 physreve 78 066705view record in web of science record created on 2009 01 12 modified on 2016 08 08

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

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

two dimensional thermal model of the finite difference lattice boltzmann method with high spatial isotropy the existing lattice boltzmann method multispeed thermal models show a limited accuracy this paper proposes a two dimensional multispeed thermal model for the finite difference lattice boltzmann method fdlbm to recover correct fluid equations up to fourth orders of local flow velocity should be retained in the local equilibrium distribution function and tensors of particle velocities should have up to seventh rank isotropy in the fdlbm particle velocities can be selected independently from the lattice configuration therefore particle velocities of octagonal directions which have up to seventh rank isotropic tensors are adopted the proposed model was verified by two simulations the model showed excellent numerical stability in addition to strict accuracy

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

essentially entropic lattice boltzmann model the entropic lattice boltzmann model elbm a discrete space time kinetic theory for hydrodynamics ensures nonlinear stability via the discrete time version of the second law of thermodynamics the h theorem compliance with the h theorem is numerically enforced in this methodology and involves a search for the maximal discrete path length corresponding to the zero dissipation state by iteratively solving a nonlinear equation we demonstrate that an exact solution for the path length can be obtained by assuming a natural criterion of negative entropy change thereby reducing the problem to solving an inequality this inequality is solved by creating a new framework for construction of pad e approximants via quadrature on appropriate convex function this exact solution also resolves the issue of indeterminacy in case of nonexistence of the entropic involution step since our formulation is devoid of complex mathematical library functions the computational cost is drastically reduced to illustrate this we have simulated a model setup of flow over the naca 0012 airfoil at a reynolds number of 2 88 ifmmode times else texttimes fi 10 6

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

truncation effect on taylor aris dispersion in lattice boltzmann schemes the taylor dispersion in parabolic velocity field provides a well known benchmark for advection diffusion ade schemes and serves as a first step towards accurate modeling of the high order non gaussian effects in heterogeneous flow while applying the lattice boltzmann ade two relaxation times trt scheme for a transport with given peclet number pe one should select six free tunable parameters namely i molecular diffusion scale equilibrium parameter ii three families of equilibrium weights assigned to the terms of mass velocity and numerical diffusion correction and iii two relaxation rates we analytically and numerically investigate the respective roles of all these degrees of freedom in the accuracy and stability in the evolution of a gaussian plume for this purpose the third and fourth order transient multi dimensional analysis of the recurrence equations of the trt ade scheme is extended for a spatially variable velocity field the key point is in the coupling of the truncation and taylor dispersion analysis which allows us to identify the second order numerical correction k t to taylor dispersivity coefficient k t the procedure is exemplified for a straight poiseuille flow where k t is given in a closed analytical form in equilibrium and relaxation parameter spaces the predicted longitudinal dispersivity is in excellent agreement with the numerical experiments over a wide parameter range in relatively small pe range the relative dispersion error increases with peclet number this deficiency reduces in the intermediate and high pe range where it becomes pe independent and velocity amplitude independent eliminating k t by a proper parameter choice and employing specular reflection for zero flux condition on solid boundaries the d2q9 trt ade scheme may reproduce the taylor aris result quasi exactly from very coarse to fine grids and from very small to arbitrarily high peclet numbers since free tunable product of two eigenfunctions also controls stability of the model the validity of the analytically established von neumann stability diagram is examined in poiseuille profile the simplest coordinate stencil subclass which is the d2q5 trt bounce back scheme demonstrates the best performance and achieves the maximum accuracy for most stable relaxation parameters closed analytical form is derived for truncation dispersivity of the d2q9 advection diffusion lbm scheme in higher peclet range its relative contribution to taylor result becomes pe and velocity independent numerical dispersivity vanishes for equilibrium velocity weight dependent eigenfunction product in trt collision analytically predicted longitudinal dispersivity is in excellent agreement with the numerical experiments the d2q5 trt bounce back scheme achieves maximum accuracy for most stable relaxation parameters

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

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

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

computing the wedderburn decomposition of group algebras by the brauer witt theorem we present an alternative constructive proof of the brauer witt theorem using the so called strongly monomial characters that gives rise to an algorithm for computing the wedderburn decomposition of semisimple group algebras of finite groups

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

characteristic nonreflecting boundary conditions for open boundaries in lattice boltzmann methods a boundary condition for lattice boltzmann methods based on the movement of information through euler characteristic directions is developed with respect to the similar conditions used in finite difference or finite volume implementations some corrections are needed to compensate the isothermal compressible nature of standard lattice boltzmann methods for fluid flow the results show that the proposed method for inlets and outlets is highly nonreflecting and mass conserving

artificial compressibility method and lattice boltzmann method similarities and differences the artificial compressibility method and the lattice boltzmann method yield the solutions of the incompressible navier stokes equations in the limit of the vanishing mach number the inclusion of the bulk viscosity is considered to be one of the reasons for the success of the lattice boltzmann method at least in the 2d case in the present paper the robustness of the artificial compressibility method is enhanced by introducing a new dissipation term which makes high cell reynolds number computation possible the increase of the stability is also confirmed in the linear stability analysis the magnitude of the eigenvalues are drastically reduced for low resolution comparisons are made with the lattice boltzmann method it is confirmed that the fortified acm is more robust as well as more accurate than the lattice boltzmann method

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

efficient kinetic method for fluid simulation beyond the navier stokes equation we present a further theoretical extension to the kinetic theory based formulation of the lattice boltzmann method of shan j fluid mech 550 413 2006 in addition to the higher order projection of the equilibrium distribution function and a sufficiently accurate gauss hermite quadrature in the original formulation a regularization procedure is introduced in this paper this procedure ensures a consistent order of accuracy control over the nonequilibrium contributions in the galerkin sense using this formulation we construct a specific lattice boltzmann model that accurately incorporates up to third order hydrodynamic moments numerical evidence demonstrates that the extended model overcomes some major defects existing in conventionally known lattice boltzmann models so that fluid flows at finite knudsen number kn can be more quantitatively simulated results from force driven poiseuille flow simulations predict the knudsen s minimum and the asymptotic behavior of flow flux at large kn

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

analysis and improvement of brinkman lattice boltzmann schemes bulk boundary interface similarity and distinctness with finite elements in heterogeneous porous media this work focuses on the numerical solution of the stokes brinkman equation for a voxel type porous media grid resolved by one to eight spacings per permeability contrast of 1 to 10 orders in magnitude it is first analytically demonstrated that the lattice boltzmann method lbm and the linear finite element method fem both suffer from the viscosity correction induced by the linear variation of the resistance with the velocity this numerical artefact may lead to an apparent negative viscosity in low permeable blocks inducing spurious velocity oscillations the two relaxation times trt lbm may control this effect thanks to free tunable two rates combination moreover the brinkman force based bf trt schemes may maintain the nondimensional darcy group and produce viscosity independent permeability provided that the spatial distribution ofis fixed independently of the kinematic viscosity such a property is lost not only in the bf bgk scheme but also by partial bounce back trt gray models as shown in this work further we propose a consistent and improved ibf trt model which vanishes viscosity correction via simple specific adjusting of the viscous mode relaxation rate to local permeability value this prevents the model from velocity fluctuations and in parallel improves for effective permeability measurements from porous channel to multidimensions the framework of our exact analysis employs a symbolic approach developed for both lbm and fem in single and stratified unconfined and bounded channels it shows that even with similar bulk discretization bf ibf and fem may manifest quite different velocity profiles on the coarse grids due to their intrinsic contrasts in the setting of interface continuity and no slip conditions while fem enforces them on the grid vertexes the lbm prescribes them implicitly we derive effective lbm continuity conditions and show that the heterogeneous viscosity correction impacts them a property also shared by fem for shear stress but in contrast with fem effective velocity conditions in lbm give rise to slip velocity jumps which depend on i neighbor permeability values ii resolution and iii control parameter ranging its reliable values from poiseuille bounce back solution in open flow to zero in darcy s limit we suggest an upscaling algorithm for from multilayers to multidimensions in random extremely dispersive samples finally on the positive side for lbm besides its overall versatility the implicit boundary layers allow for smooth accommodation of the flat discontinuous darcy profiles quite deficient in fem

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

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

recursive regularization step for high order lattice boltzmann methods a lattice boltzmann method lbm with enhanced stability and accuracy is presented for various hermite tensor based lattice structures the collision operator relies on a regularization step which is here improved through a recursive computation of nonequilibrium hermite polynomial coefficients in addition to the reduced computational cost of this procedure with respect to the standard one the recursive step allows to considerably enhance the stability and accuracy of the numerical scheme by properly filtering out second and higher order nonhydrodynamic contributions in under resolved conditions this is first shown in the isothermal case where the simulation of the doubly periodic shear layer is performed with a reynolds number ranging from 10 4 to 10 6 and where a thorough analysis of the case at text re 3 ifmmode times else texttimes fi 10 4 is conducted in the latter results obtained using both regularization steps are compared against the bhatnagar gross krook lbm for standard d2q9 and high order d2v17 and d2v37 lattice structures confirming the tremendous increase of stability range of the proposed approach further comparisons on thermal and fully compressible flows using the general extension of this procedure are then conducted through the numerical simulation of sod shock tubes with the d2v37 lattice they confirm the stability increase induced by the recursive approach as compared with the standard one

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

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

entropic multirelaxation time lattice boltzmann method for moving and deforming geometries in three dimensions entropic lattice boltzmann methods have been developed to alleviate intrinsic stability issues of lattice boltzmann models for under resolved simulations its reliability in combination with moving objects was established for various laminar benchmark flows in two dimensions in our previous work b dorschner s chikatamarla f bosch and i karlin j comput phys 295 340 2015 jctpah0021 999110 1016 j jcp 2015 04 017 as well as for three dimensional one way coupled simulations of engine type geometries in b dorschner f bosch s chikatamarla k boulouchos and i karlin j fluid mech 801 623 2016 jflsa70022 112010 1017 jfm 2016 448 for flat moving walls the present contribution aims to fully exploit the advantages of entropic lattice boltzmann models in terms of stability and accuracy and extends the methodology to three dimensional cases including two way coupling between fluid and structure and then turbulence and deforming geometries to cover this wide range of applications the classical benchmark of a sedimenting sphere is chosen first to validate the general two way coupling algorithm increasing the complexity we subsequently consider the simulation of a plunging sd7003 airfoil in the transitional regime at a reynolds number of re 40000 and finally to access the model s performance for deforming geometries we conduct a two way coupled simulation of a self propelled anguilliform swimmer these simulations confirm the viability of the new fluid structure interaction lattice boltzmann algorithm to simulate flows of engineering relevance

a structure theorem for the unit group of the integral group ring of some finite groups we classify the finite groups g such that the unit group of the integral group ring zg contains a subgroup of finite index which is the direct product of free products of abelian groups the latter problem is also investigated for any order in an arbitrary semisimple finite dimensional q algebra

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

stabilization of the lattice boltzmann method by the h theorem a numerical test for a one dimensional benchmark shock tube problem we implement the lattice boltzmann method based on the h theorem i karlin a ferrante and h c ottinger europhys lett 47 182 1999 results of simulation demonstrate significant improvement of stability as compared to realizations without explicit entropic estimations

group rings of finite strongly monomial groups central units and primitive idempotents abstract we compute the rank of the group of central units in the integral group ring z g of a finite strongly monomial group g the formula obtained is in terms of the strong shoda pairs of g next we construct a virtual basis of the group of central units of z g for a class of groups g properly contained in the finite strongly monomial groups furthermore for another class of groups g inside the finite strongly monomial groups we give an explicit construction of a complete set of orthogonal primitive idempotents of q g finally we apply these results to describe finitely many generators of a subgroup of finite index in the group of units of z g this for metacyclic groups g of the form g c q m c p n with p and q different primes and the cyclic group c p n of order p n acting faithfully on the cyclic group c q m of order q m

non classical trigonal curves we study trigonal gorenstein curves of arithmetic genus g 5 such that g has a base point through realizing them as canonical curves lying over a cone using an explicit description of such curves we compute the dimension of their moduli spaces we also investigate non classical trigonal gorenstein curves in fact we give a complete classification of such curves for arithmetic genus g 5 more generally we classify the non classical curves when the characteristic of the constant field is g 1 g 2 or 2g 3 in characteristic 2 we also solve the case g 2n 1

kinetic lattice boltzmann method for microscale gas flows issues on boundary condition relaxation time and regularization it is well known that the navier stokes equations cannot adequately describe gas flows in the transition and free molecular regimes in these regimes the boltzmann equation be of kinetic theory is invoked to govern the flows however this equation cannot be solved easily either by analytical techniques or by numerical methods hence in order to efficiently maneuver around this equation for modeling microscale gas flows a kinetic lattice boltzmann method lbm has been introduced in recent years this method is regarded as a numerical approach for solving the be in discrete velocity space with gauss hermite quadrature in this paper a systematic description of the kinetic lbm including the lattice boltzmann equation the diffuse scattering boundary condition for gas surface interactions and definition of the relaxation time is provided to capture the nonlinear effects due to the high order moments and wall boundaries an effective relaxation time and a modified regularization procedure of the nonequilibrium part of the distribution function are further presented based on previous work guo et al j appl phys 99 074903 2006 shan et al j fluid mech 550 413 2006 the capability of the kinetic lbm of simulating microscale gas flows is illustrated based on the numerical investigations of micro couette and force driven poiseuille flows

two dimensional turbulence with the lattice boltzmann equation the authors investigate the ability of the lattice boltzmann equation to reproduce the basic physics of fully turbulent two dimensional flows and present a qualitative estimate of its computational efficiency with respect to other conventional techniques