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

mean curvature flow orbits moment maps given a compact riemannian manifold together with a group of isometries we discuss mcf of the orbits and some applications e g finding minimal orbits we then specialize to lagrangian orbits in kaehler manifolds in particular in the kaehler einstein case we find a relation between mcf and moment maps which for example proves that the minimal lagrangian orbits are isolated

witten s lectures on crumpling abstract crumpling is a distortion brought about by a strong compression of a surface in which energy condenses in extremely small regions rather than being stored uniformly scaling laws describe how much energy goes into how little space as crumpling of a sheet proceeds a network of ridges and vertices develops the precise nature of these geometrical singularities depends on the stretching and bending characteristics it is shown that for two dimensional surfaces in three dimensional space energy mainly condenses in stretching ridges the scaling arguments are put on a firm basis by using the mathematical description of an elastic membrane through the von karman equations and the universal properties of ridges are discussed from this theory one can understand that crumpling confers strength finally it is sketched how energy condensation and its scaling laws depend on the dimensions of the confined sheet and embedding space

optimal low dispersion low dissipation lbm schemes for computational aeroacoustics lattice boltmzann methods lbm have been proved to be very effective methods for computational aeroacoustics caa which have been used to capture the dynamics of weak acoustic fluctuations in this paper we propose a strategy to reduce the dispersive and disspative errors of the two dimensional 2d multi relaxation time lattice boltzmann method mrt lbm by presenting an effective algorithm we obtain a uniform form of the linearized navier stokes equations corresponding to the mrt lbm in wave number space using the matrix perturbation theory and the equivalent modified equation approach for finite difference methods we propose a class of minimization problems to optimize the free parameters in the mrt lbm we obtain this way a dispersion relation preserving lbm drp lbm to circumvent the minimized dispersion error of the mrt lbm the dissipation relation precision is also improved and the stability of the mrt lbm with the small bulk viscosity is guaranteed von neuman analysis of the linearized mrt lbm is performed to validate the optimized dispersion dissipation relations considering monochromatic wave solutions meanwhile dispersion and dissipation errors of the optimized mrt lbm are quantitatively compared with the original mrt lbm finally some numerical simulations are carried out to assess the new optimized mrt lbm schemes

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

hard lefschetz theorem for valuations complex integral geometry and unitarily invariant valuations we obtain new general results on the structure of the space of translation invariant continuous valuations on convex sets a version of the hard lefschetz theorem using these and our previous results we obtain explicit characterization of unitarily invariant translation invariant continuous valuations it implies new integral geometric formulas for real submanifolds in hermitian spaces generalizing the classical kinematic formulas in euclidean

singularities structures and scaling in deformed m dimensional elastic manifolds the crumpling of a thin sheet can be understood as the condensation of elastic energy into a network of ridges that meet in vertices elastic energy condensation should occur in response to compressive strain in elastic objects of any dimension greater than 1 we study elastic energy condensation numerically in two dimensional elastic sheets embedded in spatial dimensions three or four and three dimensional elastic sheets embedded in spatial dimensions four and higher we represent a sheet as a lattice of nodes with an appropriate energy functional to impart stretching and bending rigidity minimum energy configurations are found for several different sets of boundary conditions we observe two distinct behaviors of local energy density falloff away from singular points which we identify as cone scaling or ridge scaling using this analysis we demonstrate that there are marked differences in the forms of energy condensation depending on the embedding dimension

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

the immersed boundary lattice boltzmann method for solving fluid particles interaction problems a new computational method the immersed boundary lattice boltzmann method is presented this method is a combination and utilizes the most desirable features of the lattice boltzmann and the immersed boundary methods the method uses a regular eulerian grid for the flow domain and a lagrangian grid to follow particles that are contained in the flow field the rigid body conditions for the fluid and the particles are enforced by a penalty method which assumes that the particle boundary is deformable with a high stiffness constant the velocity field of the fluid and particles is solved by adding a force density term into the lattice boltzmann equation this novel method preserves the advantages of lbm in tracking a group of particles and at the same time provides an alternative and better approach to treating the solid fluid boundary conditions the method also solves the problems of fluctuation of the forces and velocities on the particles when the bounce back boundary conditions are applied this method enables one to simulate problems with particle deformation and fluid structure deformation its results are validated by comparison with results from other methods

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

sl m c equivariant and translation covariant continuous tensor valuations abstract the space of continuous sl m c equivariant m 2 and translation covariant valuations taking values in the space of real symmetric tensors on c m r 2 m of rank r 0 is completely described the classification involves the moment tensor valuation for r 1 and is analogous to the known classification of the corresponding tensor valuations that are sl 2 m r equivariant although the method of proof cannot be adapted

integral geometry of unitary area measures abstract the existence of kinematic formulas for area measures with respect to any connected closed subgroup of the orthogonal group acting transitively on the unit sphere is established in particular the kinematic operator for area measures is shown to have the structure of a co product in the case of the unitary group the algebra associated to this co product is described explicitly in terms of generators and relations as a consequence a simple algorithm that yields explicit kinematic formulas for unitary area measures is obtained

an inverse design analysis of mesoscopic implementation of non uniform forcing in mrt lattice boltzmann models abstract in this paper the mesoscopic representation of non uniform forcing is investigated by an inverse design approach for several mrt multiple relaxation time lattice boltzmann models first the mesoscopic forcing representation of a standard lbm mrt model on a square lattice is re visited by the multiscale chapman enskog expansion we derive the most general form of the representation by taking advantage of the mrt formulation in particular we show that there are three free components in the mesoscopic representation of forcing second by the same methodology the forcing scheme of two new rectangular mrt lattice boltzmann models are derived based on the requirements of the navier stokes equations these theoretical results are then validated by numerical simulations of a forced taylor green vortex flow with several different forms of non uniform forcing to alter the kinetic energy evolution of the system the numerical results are in excellent agreement with the corresponding time dependent analytical solution of flow

a lattice boltzmann scheme of the navier stokes equation on a three dimensional cuboid lattice abstract the standard lattice boltzmann method lbm for fluid flow simulation is based on a square in 2d or a cubic in 3d lattice grids recently two new lattice boltzmann schemes have been developed on a 2d rectangular grid using the mrt multiple relaxation time collision model either by adding a free parameter in the definition of moments or by extending the equilibrium moments these models satisfy all isotropy conditions and are fully consistent to the navier stokes equations here we developed a lattice boltzmann model on a 3d cuboid lattice namely a lattice grid with different grid lengths in different spatial directions we designed the moment equations derived from our mrt lbm model through the chapman enskog analysis to be fully consistent with the navier stokes equations a second order term is added to the equilibrium moments in order to not only satisfy all isotropy conditions but also to better accommodate different values of shear and bulk viscosities the form of the second order term and the coefficients of the extended equilibrium moments are determined through an inverse design process an additional benefit of the model is that the shear viscosity can be adjusted independent of the stress moment relaxation parameter thus potentially improving the numerical stability of the model the resulting cuboid mrt lbm model is then validated through benchmark simulations using the laminar channel flow the turbulent channel flow and the 3d time dependent energy cascading taylor green vortex flow the second order accuracy of the proposed model is also demonstrated the aspect ratios for numerical stability appear to be constrained at high flow reynolds numbers especially for turbulent flow simulations an aspect requiring further investigation

geometry models of porous media based on voronoi tessellations and their porosity permeability relations in this paper we present methods that directly model the random structure of porous media using voronoi tessellations three basic structures were generated and they correspond to porous medium geometries with intersecting fractures granular interconnected tubes tubular and fibers fibrous fluid flow through these models was solved by a massively parallelized lattice boltzmann code we established the porosity permeability relations for these basic geometry models it is found that for granular and tubular geometries the specific surface area is a critical structural parameter that can bring their porosity permeability relations together under a unified kozeny carman equation a connected fracture network superimposed on the basic voronoi structure increases the dimensionless permeability relative to the kozeny carman equation isolated large pores vugs on the other hand decreases the dimensionless permeability relative to the kozeny carman equation the kozeny carman equation however cannot distinguish a heterogeneous structure with an embedded partially penetrating fracture the porosity permeability relation for fibrous geometries in general agrees with those established for simple cubic body centered cubic and face centered cubic models in the dilute limit however the dependence on the solid fraction is weaker in voronoi geometries indicating weaker hydrodynamic interactions among randomly interconnected fibers than those in the idealized models

lattice boltzmann method for the convection diffusion equation in curvilinear coordinate systems a lattice boltzmann method for simulating convection and diffusion using a curvilinear grid system is presented the proposed method does not require an interpolation or coarse graining procedure and thus maintains the algorithmic simplicity of the original lattice boltzmann scheme the lattice boltzmann scheme is based on uniformly distributed lattice points in a transformed coordinate system and the apparent anisotropy of diffusion that arises due to the coordinate transformation is properly handled using the multiple relaxation time collision operator an asymptotic analysis of the lattice boltzmann equation shows that the proposed method appropriately reproduces the transformed convection diffusion equation several specific problems are numerically analyzed in order to validate the proposed method including an axially symmetric two dimensional problem in which the diffusion flux at an oblate hemispheroid is simulated using a body fitted orthogonal curvilinear grid system

polygon based contact resolution for superquadrics the representation of discrete objects in the discrete element modelling is a fundamental issue which has a direct impact on the efficiency of discrete element implementation and the dynamic behaviour of particulate systems disks and spheres are the most commonly used geometric shapes due to their geometric simplicity and computational efficiency but they are unable to provide resistance to rolling motion for this reason some non circular spherical objects such as polygons polyhedrons superquadrics or the clustering of disks spheres to form irregular shapes are introduced when superquadrics are used as discrete elements the bottleneck of contact resolution is associated with the searching for intersections of two non linear functions which is a very expensive operation and may sometimes fail in finding the solution in this work an efficient and robust algorithm is proposed for contact resolution of 2d superquadrics in which any superquadric is approximated with a convex polygon through adaptive sampling then by clipping two polygons an efficient linear algorithm is performed to search for intersections and overlap area of the polygons the contact forces and directions are determined by employing a newly established corner corner contact model it is important to highlight that the proposed methodology can also be extended to general non circular discrete object cases the performance of the algorithm is demonstrated via numerical examples copyright 2005 john wiley sons ltd

an efficient framework for fluid structure interaction using the lattice boltzmann method and immersed moving boundaries this paper presents a serial computational framework that hydrodynamically couples the lattice boltzmann method lbm and the discrete element method dem for the solution of particle suspension problems in two and three dimensions the single relaxation time bhatnagar gross krook lbgk form of the lattice boltzmann equation is employed with an immersed moving boundary method for the fluid structure interaction similar algorithms have been previously reported in the literature however this work deliberately utilizes solution options that minimize the computational overheads of the framework to facilitate simulations of multibody structural fields in large fluid domains in particular mixed boundary conditions are employed which combine the simple bounce back technique with the immersed moving boundary method and the relatively inexpensive d3q15 lattice is employed for 3d solutions the fundamentals of the lbm are briefly discussed followed by a review of the coupling techniques available for fsi using the lbm options for mapping solid obstacles to the lbm grid are presented and an algorithm for automatic dynamic subcycling of the two explicit solution schemes is outlined the lbm dem framework is then validated and benchmarked against previously published lbm results with comments made where appropriate on the comparative accuracy and convergence characteristics finally a multi particle suspension simulation is presented to qualitatively assess the performance of the framework when a large number of dynamic contacts exist

a lattice bgk model for the navier stokes equations based on a rectangular grid abstract in this paper starting from the standard lattice bgk lbgk equation with an extended equilibrium distribution and applying the multiscale chapman enskog ce analysis we show theoretically that the correct navier stokes n s equations can be reproduced on a non standard rectangular grid using only the bgk collision model the parameters in the extended equilibrium distribution are determined through an inverse design process this new lbgk model is then validated using two benchmark cases i e the 2d decaying taylor green vortex flow and the lid driven cavity flow the accuracy and stability of the new model are discussed the new model clearly extends the standard lbgk model as it was previously thought to be impossible to construct an lbgk model for the n s equations on a rectangular grid

formulation and analysis of conserving algorithms for frictionless dynamic contact impact problems this paper presents the formulation of conserving time stepping algorithms for frictionless dynamic contact of solids a new class of finite element methods is proposed for the solution of these problems that exhibit the same conservation laws as the underlying continuum dynamical system the proposed methods are based on a penalty regularization of the constrained contact problem and lead to full conservation of the total energy of the system including the regularization penalty potential during persistent contact and restoration of the original energy upon release both linear and angular momenta are conserved by the scheme furthermore the newly developed methods have the ability to enforce the associated constraints in the velocity besides the impenetrability constraint in the displacements while preserving the conservation restoration properties of the final numerical scheme a modification of these schemes is described that assures positive energy dissipation if desired even in the highly nonlinear setting of contact impact problems leading to contact schemes with high frequency energy dissipation representative numerical simulations are presented illustrating the performance of the proposed numerical schemes

valuations on convex sets non commutative determinants and pluripotential theory abstract a new method of constructing translation invariant continuous valuations on convex subsets of the quaternionic space h n is presented in particular new examples of sp n sp 1 invariant translation invariant continuous valuations are constructed this method is based on the theory of plurisubharmonic functions of quaternionic variables developed by the author in two previous papers bull sci math 127 1 2003 1 j geom anal 13 2 2003 183

phase field lattice kinetic scheme for the numerical simulation of dendritic growth a phase field lattice kinetic model is presented for the numerical simulation of the dendritic growth of a pure crystal in the presence of thermal transport a finite difference scheme for the phase field is combined with an explicit lattice kinetic scheme for the temperature field the resulting scheme is advanced in time with an adaptive time marching procedure which permits us to achieve long simulation times with larger time steps than explicit finite difference and previous kinetic methods the method is demonstrated for the case of dendritic growth of a single crystal over a wide range of stefan and capillarity numbers

discrete thermal element modelling of heat conduction in particle systems basic formulations this paper proposes a novel numerical methodology termed the discrete thermal element method dtem for the effective modelling of heat conduction in systems comprising a large number of circular particles in 2d cases based on an existing analytical integral solution for the temperature distribution over a circular domain subjected to the neumann boundary condition a linear algebraic system of thermal conductivity equations for each particle is derived in terms of the average temperatures and the resultant fluxes at the contact zones with its neighboring particles thus each particle is treated as an individual element with the number of temperature unknowns equal to the number of particles that it is in contact with the element thermal conductivity matrix can be very effectively evaluated and is entirely dependent on the characteristics of the contact zones including the contact positions and contact angles this new element shares the same form and properties with its conventional thermal finite element counterpart in particular the whole solution procedure can follow exactly the same steps as those involved in the finite element analysis unlike finite elements or other modern numerical techniques however no discretization errors are involved in the discrete thermal elements the modelling error mainly stems from the assumption made about the heat flux distribution within the contact zones based on some theoretical work an enhanced version is suggested to improve the approximation the numerical assessment against finite element results indicates that the basic version of dtem can achieve a very reasonable solution accuracy while the enhanced version further improves the accuracy to a high level in addition thermal resistance phenomena between the contact zones can be readily incorporated into the current modelling framework

energy conserving lattice boltzmann thermal model in two dimensions a discrete velocity model is presented for lattice boltzmann thermal fluid dynamics this model is implemented and tested in two dimensions with a finite difference scheme comparison with analytical solutions shows an excellent agreement even for wide temperature differences an alternative approximate approach is then presented for traditional lattice transport schemes

a hierarchy of plate models derived from nonlinear elasticity by gamma convergence we derive a hierarchy of plate models from three dimensional nonlinear elasticity by convergence what distinguishes the different limit models is the scaling of the elastic energy per unit volume h where h is the thickness of the plate this is in turn related to the strength of the applied force h membrane theory derived earlier by le dret and raoult corresponds to 0 nonlinear bending theory to 2 von karman theory to 3 4 and linearized vk theory to 3 intermediate values of lead to certain theories with constraints a key ingredient in the proof is a generalization to higher derivatives of our rigidity result 29 which states that for maps v 0 1 3 3 the l2 distance of v from a single rotation is bounded by a multiple of the l2 distance from the set so 3 of all rotations

difference bodies in complex vector spaces abstract a complete classification is obtained of continuous translation invariant minkowski valuations on an m dimensional complex vector space which are covariant under the complex special linear group

design of energy conserving algorithms for frictionless dynamic contact problems this paper proposes a formulation of dynamic contact problems which enables exact algorithmic conservation of linear momentum angular momentum and energy in finite element simulations it is seen that a lagrange multiplier enforcement of an appropriate contact rate constraint produces these conservation properties a related method is presented in which a penalty regularization of the aforementioned rate constraint is utilized this penalty method sacrifices the energy conservation property but is dissipative under all conditions of changing contact so that the global algorithm remains stable notably it is also shown that augmented lagrangian iteration utilizing this penalty kernel reproduces the energy conserving i e lagrange multiplier solution to any desired degree of accuracy the result is a robust stable method even in the context of large deformations as is shown by some representative numerical examples in particular the ability of the formulation to produce accurate results where more traditional integration schemes fail is emphasized by the numerical simulations 1997 by john wiley sons ltd

immersed boundary lattice boltzmann model based on multiple relaxation times as an alterative version of the lattice boltzmann models the multiple relaxation time mrt lattice boltzmann model introduces much less numerical boundary slip than the single relaxation time srt lattice boltzmann model if some special relationship between the relaxation time parameters is chosen on the other hand most current versions of the immersed boundary lattice boltzmann method which was first introduced by feng and improved by many other authors suffer from numerical boundary slip as has been investigated by le and zhang to reduce such a numerical boundary slip an immerse boundary lattice boltzmann model based on multiple relaxation times is proposed in this paper a special formula is given between two relaxation time parameters in the model a rigorous analysis and the numerical experiments carried out show that the numerical boundary slip reduces dramatically by using the present model compared to the single relaxation time based model

contact impact by the pinball algorithm with penalty and lagrangian methods contact impact algorithms which are sometimes called slideline algorithms are a computationally time consuming part of many explicit simulations of non linear problems because they involve many branches so they are not amenable to vectorization which is essential for speed on supercomputers the pinball algorithm is a simplified slideline algorithm which is readily vectorized its major idea is to embed pinballs in surface elements and to enforce the impenetrability condition only to pinballs it can be implemented in either a lagrange multiplier or penalty method it is shown that in any lagrange multiplier method no iterations are needed to define the contact surface examples of solutions and running times are given

a multi relaxation lattice kinetic method for passive scalar diffusion a kinetic lattice boltzmann scheme for advection diffusion is presented the scheme is based on a matrix formulation of the lattice boltzmann method which permits to handle non isotropic diffusion advection problems in addition by adjusting the kinetic eigenvectors defining the collision matrix to the local value of the flow velocity the scheme is also shown to preserve isotropy under genuinely two dimensional flow

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

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

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

combined three dimensional lattice boltzmann method and discrete element method for modelling fluid particle interactions with experimental assessment a general algorithmic framework is established in this paper for numerical simulations of three dimensional fluid particle interaction problems with a large number of moving particles in turbulent flows using a combined lattice boltzmann method lbm and discrete element method dem in this approach the fluid field is solved by the extended three dimensional lbm with the incorporation of the smagorinsky turbulence model while particle interactions are modelled by the dem the hydrodynamic interactions between fluid and particles are realized through the extension of an existing two dimensional fluid particle hydrodynamic interaction scheme the main computational aspects comprise the lattice boltzmann formulation for the solution of fluid flows the incorporation of a large eddy simulation based turbulence model within the framework of the three dimensional lbm for turbulent flows the moving boundary condition for hydrodynamic interactions between fluid and moving particles and the discrete element modelling of particle particle interactions to assess the solution accuracy of the proposed approach a much simplified laboratory model of vacuum dredging systems for mineral recovery is employed the numerical results are compared with the experimental data available it shows that the overall correspondence between numerical results and experimental measurements is good and thus indicates to a certain extent the solution accuracy of the proposed methodology copyright 2009 john wiley sons ltd

rectangular lattice boltzmann method a set of rectangular lattice boltzmann methods for fluid flows is developed it is shown that reformulating local equilibrium distribution functions can result in the rectangular lattice boltzmann models without the aid of an interpolation for shallow water equations navier stokes equations and axisymmetric flow equations in addition schemes for correct incorporation of force terms into the models are proposed for simulations of flows involving forces in practice the methods completely retain the innate kinetic features and the simple procedure of the standard lattice boltzmann method with an additional benefit of being suitable for rectangular lattices at little extra computational cost the methodology is illustrated and validated through its application to different flow problems demonstrating the potential power of the models

lattice boltzmann method for groundwater flow in non orthogonal structured lattices the efficiency of the lattice boltzmann method lbm in modeling isotropic groundwater flow in domains of arbitrary geometry has been investigated the poisson equation was transformed in general curvilinear coordinates the corresponding equilibrium function for the d2q9 square lattice based on metric function between the physical and the computational domain has been established the resulting lbm was checked on examples having higher generality flows in confined and unconfined aquifers in vertical and horizontal plane have been considered in addition the phreatic water table representing upper boundary in the vertical plane was determined by the dynamic stretching approach not requiring complex concepts for dealing with the free surface like the volume of fluid method the accuracy and stability of the model is controlled by the adaptive mesh concept this allows application of higher density grid in critical areas with high pressure and velocity gradients and vice versa the number of computation points is significantly reduced without loosing accuracy the basic characteristics of the lbm including features like parallelization and simplicity are maintained the advantages of the proposed curvilinear lbm in modeling groundwater flow in domains of complex shape over the former published methods is demonstrated by three examples

a theorem on geometric rigidity and the derivation of nonlinear plate theory from three dimensional elasticity the energy functional of nonlinear plate theory is a curvature functional for surfaces rst proposed on physical grounds by g kirchhoff in 1850 we show that it arises as a 0 limit of three dimensional nonlinear elasticity theory as the thickness of a plate goes to zero a key ingredient in the proof is a sharp rigidity estimate for maps v v u r n u r n we show that the l 2 distance of rv from a single rotation matrix is bounded by a multiple of the l 2 distance from

on the central difference algorithm in discrete element modelling of impact the paper provides a comprehensive analysis of the accuracy and stability of the central difference scheme when applied to simulate a simple impact problem in the context of the discrete element approach it is revealed that the algorithm exhibits some different behaviour due to the inherent nonlinearity discontinuity of the impact system particularly for an elastic or slightly inelastic impact the stable unstable region governing the selection of a maximum time step size is essentially different from that defined by the conventional linear stability criterion and thus a smaller time step should be employed in order to reduce the possible occurrence of an unexpected numerical instability

on the sobolev space of isometric immersions we prove that every w 2 2 isometric immersion from a convex regular domain of r 2 into r3 can be approximated in w 2 2 norm by smooth isometric immersions from the same domain into r3

efficient uncertainty quantification for permeability of three dimensional porous media through image analysis and pore scale simulations in this paper we propose an efficient coupled approach for uncertainty quantification of permeability for randomly reconstructed three dimensional 3d pore images where the porosity and two point correlations of a realistic sandstone sample are honored the joshi quiblier adler approach and karhunen loeve expansion are utilized for quick reconstruction of 3d pore images with reduced random dimensionality the eigenvalue problem for the covariance matrix of 3d intermediate gaussian random fields is solved equivalently by a kernel method then the lattice boltzmann method is adopted to simulate fluid flow in reconstructed pore space and evaluate permeability lastly the sparse polynomial chaos expansion sparse pce integrated with a feature selection method is employed to predict permeability distributions incurred by the randomness in microscopic pore structures the feature selection process which is intended to discard redundant basis functions is carried out by the least absolute shrinkage and selection operator modified least angle regression along with cross validation the competence of our proposed approach is validated by the results from monte carlo simulation it reveals that a small number of samples is sufficient for sparse pce with feature selection to produce convincing results then we utilize our method to quantify the uncertainty of permeability under different porosities and correlation parameters it is found that the predicted permeability distributions for reconstructed 3d pore images are close to experimental measurements of berea sandstones in the literature in addition the results show that porosity and correlation length are the critical influence factors for the uncertainty of permeability

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

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

shift an implementation for lattice boltzmann simulation in low porosity porous media the lattice boltzmann lb method has proven to be a promising method for simulating fluid dynamics in porous media when fluid flow in pores is the only concern a standard lb implementation which stores one or two sets of particle distribution functions pdfs for both pore and solid cells wastes a large amount of memory especially for low porosity media this paper proposes a lb implementation scheme that stores a single set of pdfs for pore cells only and therefore makes it possible to simulate flow through larger and more realistic porous models a unique feature of this scheme is that it decomposes all pdfs into a set of 1d arrays in such a way that each array corresponds to a set of pore cells that connect one another along a pair of opposite lb velocity directions this allows lb propagation and a standard bounce back rule to be realized together as one or two circular shifting operations on every array for this reason this scheme is called shift although pdfs are not stored in an efficient way for lb collision operation it is shown that the incurred overhead could be reduced by properly arranging pdf arrays according to the pore structures a d3q15 lb implementation of shift using the lattice bhatnagar gross krook model is applied to simulate the stokes flow through models of four natural and synthetic rock samples with porosities ranging from about 10 to 38 results show that shift requires 36 82 less memory than a comparable d3q15 lb does which stores a single set of pdf for both pore and solid cells shift achieves minimum performances of over 11 and 3 8 mega lattice updates per second mlups for the combined propagation and bounce back operation and the collision operation respectively and therefore a minimum of 2 8 mlups in total on a computer with one amd opteron 2218 the performance of the collision operation is significantly improved for all cases when a simple k mean clustering technique is employed to rearrange pdf arrays it is argued and shown that the number of pdf arrays per pore cell and the length frequency of pdf arrays are useful measurements on the geometry and topology of the pore structures and these characteristics are able to explain shift performance variations

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

improved implicit integrators for transient impact problems geometric admissibility within the conserving framework the value of energy and momentum conserving algorithms has been well established for the analysis of highly non linear systems including those characterized by the nonsmooth non linearities of an impact event this work proposes an improved integration scheme for frictionless dynamic contact seeking to preserve the stability properties of exact energy and momentum conservation without the heretofore unavoidable compromise of violating geometric admissibility as established by the contact constraints the physically motivated introduction of a discrete contact velocity provides an algorithmic framework that ensures exact conservation locally while remaining independent of the choice of constraint treatment thus making full conservation equally possible in conjunction with a penalty regularization as with an exact lagrange multiplier enforcement the discrete velocity effects are incorporated as a post convergence update to the system velocities and thus have no direct effect on the non linear solution of the displacement equilibrium equation the result is a robust implicit algorithmic treatment of dynamic frictionless impact appropriate for large deformations and fully conservative for a range of geometric constraints copyright 2001 john wiley sons ltd

lattice boltzmann simulations of a time dependent natural convection problem a two dimensional double multiple relaxation time thermal lattice boltzmann method is used to simulate natural convection flows in differentially heated cavities the buoyancy effects are considered under the boussinesq assumption flow and temperature fields are respectively solved with nine and five discrete velocities models boundary conditions are implemented with the classical bounce back or an on node approach the latter uses the popular zou and he and counter slip formulations this paper evaluates the differences between the two implementations for steady and time dependent flows as well as the space and time convergence orders

kinematic formulas on the quaternionic plane we introduce different bases for the vector space of sp 2 sp 1 invariant translation invariant continuous valuations on the quaternionic plane and determine a complete set of kinematic formulas

consistent lattice boltzmann schemes for the brinkman model of porous flow and infinite chapman enskog expansion we show that a consistent modeling of porous flows needs at least one free collision relaxation rate to avoid a nonlinear dependency of the numerical errors on the viscosity this condition is necessary to get the viscosity independent permeability from the stokes flow and to parametrize properly with nondimensional physical numbers the lattice boltzmann brinkman schemes the two relaxation time trt collision operator controls all coefficients of the higher order corrections in steady solutions with a specific combination of its two collision rates a possibility lacking for the bhatnagar gross krook bgk based single relaxation time schemes the analysis is based on exact recurrence equations of the evolution equation and illustrated for the exact solutions of the brinkman scheme in simply oriented parallel and diagonal channels the apparent viscosity coefficient of the trt stokes brinkman scheme in arbitrary flow is only approximated the compatibility of one dimensional arbitrarily rotated flows with the nonlinear navier stokes equilibrium is examined an explicit dependency for all coefficients on the relaxation rates is presented for the infinite steady state chapman enskog expansion

contravariant minkowski valuations a complete classification of all continuous gl n contravariant minkowski valuations is established as an application we present a family of sharp isoperimetric inequalities for such valuations which generalize the classical petty projection inequality

derivation of the lattice boltzmann method by means of the discrete ordinate method for the boltzmann equation in this note we show that the lattice boltzmann bgk method in common use can be derived from the boltzmann equation itself according to the present derivation it is apparent that the equation thus derived can be reduced to the navier stokes equation at a limit of small knudsen number since the equation thus derived is the boltzmann equation itself hence the present derivation method gives us a simple and flexible recipe to construct the lattice boltzmann method and makes it easy to construct an extended lattice boltzmann method in various ways 15 refs 1 fig

crofton measures and minkowski valuations a description of continuous rigid motion compatible minkowski valuations is established as an application we present a brunn minkowski type inequality for intrinsic volumes of these valuations

continuous rotation invariant valuations on convex sets the notion of valuation on convex sets can be considered as a generalization of the notion of measure which is deflned only on the class of convex compact sets it is well known that there are important and interesting examples of valuations on convex sets which are not measures in the usual sense as for example the mixed volumes basic deflnitions and some classical examples are discussed in section 2 of this paper for more detailed information we refer to the surveys mc sch and mc3 throughout this paper all the valuations are assumed to be continuous with respect to the hausdorfi metric note that the theory of valuations which are invariant or covariant with respect to translations belongs to the classical part of convex geometry there exists an explicit description of translation invariant continuous valuations on 1 and 2 due to hadwiger h1 the case of 2 is nontrivial continuous rigid motion invariant valuations on d are completely classifled by the remarkable hadwiger theorem as linear combinations of the quermassintegrals cf h2 or for a simpler proof k

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

even valuations on convex bodies the notion of eveil valuation is introduced as a natural generalization of volume on cornpact convex subsets of euclidean space a recent characterization theorem for volume leads in turn to a connection between even valuations on compact convex sets and continuous functions on grassmannians this connection can be described in part using generating distributions for symmetric compact convex sets we also explore some consequences of these characterization results in convex and integral geometry recent interest in volume as a valuation on compact conlvex sets stems from hilbert s third problem which is actually an ancient problem recast in modern terms hilbert asked if two polytopes p and q can be each cut into a finite number of pieces p pn and q qm with each pi congruent to qi by a rigid euclidean motion provided that p and q have the same volume 18 this question was answered in the negative by max dehn 2 4 29 who found a functionlal on polytopes that is invariant under dissections over rigid motions while varying in value among polytopes of equal volume in other words the dehn invariant is a simple rigid motion invariant valuation on polytopes that is not equal to volume under any normalization dehn s solution left open the question of exactly what conditions oil p and q imply equidissectability over the group of rigid motions although this problem was solved by hadwiger in the case where only translations and no rotations nor reflections are permitted see 2 16 17 26 29 in the course of studying this and related problems hadwiger discovered a characterization of euclidean volume as a continuous rigid motion invariant simple valuation on compact convex sets that is a continuous rigid motion invariant valuation that vanishes on convex sets of less than full dimension this result led in turn to a complete characterization of all continuous rigid motion inivariant valuations on compact convex sets in 1r as consisting of a real n 4 dimensional vector space spanned by the intrinsic volumes or quermassintegrals 16 also 20 21 31 since many standard functionals and integral operators can be interpreted as invariant valuations such as intrinsic volumes mean projections crofton and kinematic formulas what came to be known as hadwiger s chtracterization theorem proved to be a valuable tool for generating quick and effortless proofs of many formulas and equations in integral geometry unfortunately hadwiger s original proof was long and difficult 161 while seeking a shorter proof of hadwiger s volume characterization the author discovered received by the editors june 24 1996 and in revised form september 29 1997 1991 mathematics subject classification primary 52a22 52a38 52a39 52b45 research supported in part by nsf grants dms 9022140 to msri and dms 9626688 to the author 1999 american mathematical society 71 this content downloaded from 207 46 13 52 on mon 24 oct 2016 04 15 57 utc all use subject to http about jstor org terms

coupled lattice boltzmann method and discrete element modelling of particle transport in turbulent fluid flows computational issues this paper presents essential numerical procedures in the context of the coupled lattice boltzmann lb and discrete element de solution strategy for the simulation of particle transport in turbulent fluid flows key computational issues involved are 1 the standard lb formulation for the solution of incompressible fluid flows 2 the incorporation of large eddy simulation les based turbulence models in the lb equations for turbulent flows 3 the computation of hydrodynamic interaction forces of the fluid and moving particles and 4 the de modelling of the interaction between solid particles a complete list is provided for the conversion of relevant physical variables to lattice units to facilitate the understanding and implementation of the coupled methodology additional contributions made in this work include the application of the smagorinsky turbulence model to moving particles and the proposal of a subcycling time integration scheme for the de modelling to ensure an overall stable solution a particle transport problem comprising 70 large particles and high reynolds number around 56 000 is provided to demonstrate the capability of the presented coupling strategy copyright 2007 john wiley sons ltd

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

projection bodies in complex vector spaces the space of minkowski valuations on an m dimensional complex vector space which are continuous translation invariant and contravariant under the complex special linear group is explicitly described each valuation with these properties is shown to satisfy geometric inequalities of the brunn minkowski aleksandrov fenchel and minkowski type

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

lattice boltzmann equation on a two dimensional rectangular grid abstract we construct a multirelaxation lattice boltzmann model 1 on a two dimensional rectangular grid the model is partly inspired by a previous work of koelman 2 to construct a lattice bgk model on a two dimensional rectangular grid the linearized dispersion equation is analyzed to obtain the constraints on the isotropy of the transport coefficients and galilean invariance for various wave propagations in the model the linear stability of the model is also studied the model is numerically tested for three cases a a vortex moving with a constant velocity on a mesh with periodic boundary conditions b poiseuille flow with an arbitrary inclined angle with respect to the lattice orientation and c a cylinder asymmetrically placed in a channel the numerical results of these tests are compared with either analytic solutions or the results obtained by other methods satisfactory results are obtained for the numerical simulations

contact measures in isotropic spaces abstract we revisit the contact measures introduced by firey and further developed by schneider and teufel from the perspective of the theory of valuations on manifolds this reveals a link between the kinematic formulas for area measures studied by wannerer and the integral geometry of curved isotropic spaces as an application we find explicitly the kinematic formula for the surface area measure in hermitian space

three dimensional multi relaxation time mrt lattice boltzmann models for multiphase flow in this paper three dimensional 3d multi relaxation time mrt lattice boltzmann lb models for multiphase flow are presented in contrast to the bhatnagar gross krook bgk model a widely employed kinetic model in mrt models the rates of relaxation processes owing to collisions of particle populations may be independently adjusted as a result the mrt models offer a significant improvement in numerical stability of the lb method for simulating fluids with lower viscosities we show through the chapman enskog multiscale analysis that the continuum limit behavior of 3d mrt lb models corresponds to that of the macroscopic dynamical equations for multiphase flow we extend the 3d mrt lb models developed to represent multiphase flow with reduced compressibility effects the multiphase models are evaluated by verifying the laplace young relation for static drops and the frequency of oscillations of drops the results show satisfactory agreement with available data and significant gains in numerical stability

the cos λ and sin λ transforms as intertwining operators between generalized principal series representations of sl n 1 k abstract in this article we connect topics from convex and integral geometry with well known topics in representation theory of semisimple lie groups by showing that the cos and sin transforms on the grassmann manifolds gr p k su n 1 k s u p k u n 1 p k are standard intertwining operators between certain generalized principal series representations induced from a maximal parabolic subgroup p p of sl n 1 k the index p indicates the dependence of the parabolic on p the general results of knapp and stein 1971 1980 20 21 and vogan and wallach 1990 44 then show that both transforms have meromorphic extension to c and are invertible for generic c furthermore known methods from representation theory combined with a selberg type integral allow us to determine the k spectrum of those operators

improved coupling of time integration and hydrodynamic interaction in particle suspensions using the lattice boltzmann and discrete element methods this paper introduces improvements to the simulation of particle suspensions using the lattice boltzmann method lbm and the discrete element method dem first the benefit of using a two relaxation time trt collision operator instead of the popular bhatnagar gross krook bgk collision operator is demonstrated second a modified solid weighting function for the partially saturated method psm for fluid solid interaction is defined and tested results are presented for a range of flow configurations including sphere packs duct flows and settling spheres with good accuracy and convergence observed past research has shown that the drag and consequently permeability predictions of the lbm exhibit viscosity dependence when used with certain boundary conditions such as bounce back or interpolated bounce back and this is most pronounced when the bgk collision operator is employed the improvements presented here result in a range of computational viscosities and therefore relaxation parameters within which drag and permeability predictions remain invariant this allows for greater flexibility in using the relaxation parameter to adjust the lbm timestep which can subsequently improve synchronisation with the time integration of the dem this has significant implications for the simulation of large scale suspension phenomena where the limits of computational hardware persistently constrain the resolution of the lbm lattice c 2018 elsevier ltd all rights reserved

hermitian integral geometry we give in explicit form the principal kinematic formula for the action of the ane unitary group on c n together with a straightforward algebraic method for computing the full array of unitary kinematic formulas expressed in terms of certain convex valuations introduced essentially by h tasaki we introduce also several other canonical bases for the algebra of unitary invariant valuations explore their interrelations and characterize in these terms the cones of positive and monotone elements

wall model for large eddy simulation based on the lattice boltzmann method an original wall model for lattice boltzmann based large eddy simulation is presented it relies on either an analytical profile for the velocity profile within the first off wall cell or the solution of turbulent boundary layer equations the latter are solved thanks to a meshless approach to obtain a user friendly method the proposed method is observed to be both robust and accurate yielding very satisfactory results in plane channel flow up to re email protected 000 on uniform grids with dx email protected email protected 1000 the computed maximum error on skin friction is about 4 in most investigated cases on the coarsest grids 10 grid points across the half channel height it lies within 1 2 on finer grids with 20 60 uniformly distributed grid points in the channel half height

lattice boltzmann simulations of 2d laminar flows past two tandem cylinders we apply the lattice boltzmann equation lbe with multiple relaxation time mrt collision model to simulate laminar flows in two dimensions 2d in order to simulate flows in an unbounded domain with the lbe method we need to address two issues stretched non uniform mesh and inflow and outflow boundary conditions we use the interpolated grid stretching method to address the need of non uniform mesh we demonstrate that various inflow and outflow boundary conditions can be easily and consistently realized with the mrt lbe the mrt lbe with non uniform stretched grids is first validated with a number of test cases the poiseuille flow the flow past a cylinder asymmetrically placed in a channel and the flow past a cylinder in an unbounded domain we use the lbe method to simulate the flow past two tandem cylinders in an unbounded domain with re 100 our results agree well with existing ones through this work we demonstrate the effectiveness of the mrt lbe method with grid stretching

a hydrodynamically consistent mrt lattice boltzmann model on a 2d rectangular grid a multiple relaxation time mrt lattice boltzmann lb model on a d2q9 rectangular grid is designed theoretically and validated numerically in the present work by introducing stress components into the equilibrium moments this mrt lb model restores the isotropy of diffusive momentum transport at the macroscopic level or in the continuum limit leading to moment equations that are fully consistent with the navierstokes equations the model is derived by an inverse design process which is described in detail except one moment associated with the energy square all other eight equilibrium moments can be theoretically and uniquely determined the model is then carefully validated using both the two dimensional decaying taylorgreen vortex flow and lid driven cavity flow with different grid aspect ratios the corresponding results from an earlier model bouzidi et al 2001 28 are also presented for comparison the results of bouzidi et al s model show problems associated with anisotropy of viscosity coefficients while the present model exhibits full isotropy and is accurate and stable

classification of invariant valuations on the quaternionic plane abstract we describe the orbit space of the action of the group sp 2 sp 1 on the real grassmann manifolds gr k h 2 in terms of certain quaternionic matrices of moore rank not larger than 2 we then give a complete classification of valuations on the quaternionic plane h 2 which are invariant under the action of the group sp 2 sp 1

valuation theory of indefinite orthogonal groups abstract let so p q denote the identity connected component of the real orthogonal group with signature p q we give a complete description of the spaces of continuous and generalized translation and so p q invariant valuations generalizing hadwiger s classification of euclidean isometry invariant valuations as a result of independent interest we identify within the space of translation invariant valuations the class of klain schneider continuous valuations which strictly contains all continuous translation invariant valuations the operations of pull back and push forward by a linear map extend naturally to this class

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

lattice boltzmann model for complex ginzburg landau equation in curvilinear coordinates a lattice boltzmann model is proposed for solving the complex ginzburg landau equation cgle with curvilinear coordinates the method maintains the algorithmic simplicity of the original lattice boltzmann scheme and does not require an interpolation or coarse graining procedure this lattice boltzmann scheme is based on uniformly distributed lattice points in these curvilinear coordinate systems the algorithm provides advantages similar to the previous lattice boltzmann method in that it is easily adapted to cgle the numerical simulations show spiral wave on a disc the surface of a sphere and the inside of a sphere examples show that the model accurately reproduces the phenomena in the cgle