lattice boltzmann scheme for mixture modeling analysis of the continuum diffusion regimes recovering maxwell stefan model and incompressible navier stokes equations a finite difference lattice boltzmann scheme for homogeneous mixture modeling which recovers maxwell stefan diffusion model in the continuum limit without the restriction of the mixture averaged diffusion approximation was recently proposed p asinari phys rev e 77 056706 2008 the theoretical basis is the bhatnagar gross krook type kinetic model for gas mixtures p andries k aoki and b perthame j stat phys 106 993 2002 in the present paper the recovered macroscopic equations in the continuum limit are systematically investigated by varying the ratio between the characteristic diffusion speed and the characteristic barycentric speed it comes out that the diffusion speed must be at least one order of magnitude in terms of knudsen number smaller than the barycentric speed in order to recover the navier stokes equations for mixtures in the incompressible limit some further numerical tests are also reported in particular 1 the solvent and dilute test cases are considered because they are limiting cases in which the maxwell stefan model reduces automatically to fickian cases moreover 2 some tests based on the stefan diffusion tube are reported for proving the complete capabilities of the proposed scheme in solving maxwell stefan diffusion problems the proposed scheme agrees well with the expected theoretical results

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

complete integrability of the kortweg de vries equation under perturbation around its solution lie backlund symmetry approach it is shown that when the korteweg de vries equation is perturbed about a particular solution the resulting evolution equations to all order of perturbations admit infinitely many lie backlund symmetries the corresponding commuting constants of motion are derived and thereby complete integrability can be established

from the boltzmann equations to the equations of incompressible fluid mechanics i we consider here the problem of deriving rigorously from boltzmann s equation globally in time and for general initial conditions fluid mechanics equations such as the navier stokes or euler equations

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

a lattice boltzmann method for immiscible two phase stokes flow with a local collision operator we propose a lattice boltzmann model for immiscible two phase stokes flow with a local collision operator the model is based on two different lattice boltzmann automata one for the flow field and one for an indicator function for the two different phases the model is described in detail and verified by the following test cases a static bubble for the surface tension a closed capillary tube for the contact angle and two phase flow in a concentric annulus for the viscosity ratio in the appendix an asymptotic analysis for the derivation of the two phase stokes equation is given

boundary conditions for the upwind finite difference lattice boltzmann model evidence of slip velocity in micro channel flow we conduct a systematic study of the effect of various boundary conditions bounce back and three versions of diffuse reflection for the two dimensional first order upwind finite difference lattice boltzmann model simulation of couette flow in a micro channel using the diffuse reflection boundary condition reveals the existence of a slip velocity that depends on the knudsen number e l l where l is the mean free path and l is the channel width for walls moving in opposite directions with speeds u w the slip velocity satisfies u s l i p 2 eu w a l l 1 2 e in the case of poiseuille flow in a micro channel the slip velocity is found to depend on the lattice spacing ds and knudsen number e to both first and second order the best results are obtained for diffuse reflection boundary conditions that allow thermal mixing at a wall located at half lattice spacing outside the boundary nodes

fixed grid fluid structure interaction in two dimensions based on a partitioned lattice boltzmann and p fem approach over the last decade the lattice boltzmann method which was derived from the kinetic gas theory has matured as an efficient approach for solving navier stokes equations the p fem approach has proved to be highly efficient for a variety of problems in the field of structural mechanics our goal is to investigate the validity and efficiency of coupling the two approaches to simulate transient bidirectional fluid structure interaction problems with geometrically non linear structural deflections a benchmark configuration of self induced large oscillations for a flag attached to a cylinder can be accurately and efficiently reproduced within this setting we describe in detail the force evaluation techniques displacement transfers and the algorithm used to couple these completely different solvers as well as the results and compare them with a benchmark reference solution computed by a monolithic finite element approach copyright 2009 john wiley sons ltd

asymptotic analysis of lattice boltzmann boundary conditions in this article we use a general method for the analysis of finite difference schemes to investigate lattice boltzmann algorithms for navier stokes problems with dirichlet boundary conditions several link based boundary conditions for commonly used lattice boltzmann bgk models are considered with our method the accuracy of the algorithms can be exactly predicted moreover the analytical results can be used to construct new algorithms which is demonstrated with a corrected bounce back rule that requires only local evaluations but still yields second order accuracy for the velocity the analysis is applicable to general geometries and instationary flows

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

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

a discrete variational identity on semi direct sums of lie algebras the discrete variational identity under general bilinear forms on semi direct sums of lie algebras is established the constant involved in the variational identity is determined through the corresponding solution to the stationary discrete zero curvature equation an application of the resulting variational identity to a class of semi direct sums of lie algebras in the volterra lattice case furnishes hamiltonian structures for the associated integrable couplings of the volterra lattice hierarchy

a lattice boltzmann front tracking method for interface dynamics with surface tension in two dimensions we propose to combine the lattice boltzmann equation lbe and the front tracking ft method to simulate interfacial dynamics with surface tension in two dimensions 2d in the proposed lbe ft method the flow is modeled by the lbe on a fixed cartesian mesh whereas interfaces are explicitly tracked by a set of markers that are advected by the flow the interface curvature is computed from adjacent markers and is then used to determine surface tension according to laplace s law the local capillary forces evaluated at the markers are distributed to nearby eulerian grid points according to a smearing function to approximate the dirac delta function due to peskin to validate the proposed lbe ft method we simulate 1 a circular bubble in a flow either quiescent or moving with a constant velocity and 2 the decaying capillary waves at the interface of two fluids of equal viscosities and densities for the circular bubble the spurious current measured in the lbe ft is weaker than that observed in the standard volume of fluid method and some existing lbe models for the capillary waves the numerical results of the period t or frequency the attenuation rate the surface tension and the root mean square error of the wave amplitude agree well with the normal mode and prosperetti s solutions the proposed lbe ft method is shown to have a second order rate of convergence we also show that the lbe ft method is superior to the existing lattice bgk diffusive interface method in terms of accuracy of interface representation numerical stability and computational efficiency

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

a family of liouville integrable lattice equations with a parameter and its two symmetry constraints a two by two matrix spectral problem with an arbitrary constant is introduced a family of integrable lattice equations involving a parameter is derived by the technique of lax pairs the typical lattice equation in the obtained family is a deformed toda lattice system the bi hamiltonian structure of the obtained family of integrable lattice equations is established by using the discrete trace identity and we prove the liouville integrability of obtained family of integrable lattice equations then bargmann symmetry constraint and an implicit symmetry constraint of the obtained family are presented by binary nonlinearization method under these two symmetry constraints we obtain two series of integrable symplectic maps and two sequences of completely integrable finite dimensional hamiltonian systems in liouville sense and every integrable lattice equation in the obtained family is decomposed by an integrable symplectic map and a completely integrable finite dimensional hamiltonian system as a specia

dynamic subgrid scale modeling of turbulent flows using lattice boltzmann method abstract in this paper we discuss the incorporation of dynamic subgrid scale sgs models in the lattice boltzmann method lbm for large eddy simulation les of turbulent flows the use of a dynamic procedure which involves sampling or test filtering of super grid turbulence dynamics and subsequent use of scale invariance for two levels circumvents the need for empiricism in determining the magnitude of the model coefficient of the sgs models we employ the multiple relaxation times mrt formulation of lbm with a forcing term which has improved physical fidelity and numerical stability achieved by proper separation of relaxation time scales of hydrodynamic and non hydrodynamic modes for simulation of the grid filtered dynamics of large eddies the dynamic procedure is illustrated for use with the common smagorinsky eddy viscosity sgs model and incorporated in the lbm kinetic approach through effective relaxation time scales the strain rate tensor in the sgs model is locally computed by means of non equilibrium moments of the mrt lbm we also discuss proper sampling techniques or test filters that facilitate implementation of dynamic models in the lbm for accommodating variable resolutions we employ conservative locally refined grids in this framework as examples we consider the canonical anisotropic and inhomogeneous turbulent flow problem i e fully developed turbulent channel flow at two different shear reynolds numbers r e of 180 and 395 the approach is able to automatically and self consistently compute the values of the smagorinsky coefficient c s in particular the computed value in the outer or bulk flow region where turbulence is generally more isotropic is about 0 155 or the model coefficient c c s 2 0 024 which is in good agreement with prior data it is also shown that the model coefficient becomes smaller and approaches towards zero near walls reflecting the dampening of turbulent length scales near walls the computed turbulence statistics at these reynolds numbers are also in good agreement with prior data the paper also discusses a procedure for incorporation of more general scale similarity based sgs stress models

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

a modified toda spectral problem and its hierarchy of bi hamiltonian lattice equations starting from a modified toda spectral problem a hierarchy of generalized toda lattice equations with two arbitrary constants is constructed through discrete zero curvature equations it is shown that the hierarchy possesses a bi hamiltonian structure and a hereditary recursion operator which implies that there exist infinitely many common commuting symmetries and infinitely many common commuting conserved functionals two cases of the involved constants present two specific integrable sub hierarchies one of which is exactly the toda lattice hierarchy

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

n shift cross orthogonal sequences n shift cross orthogonal sequences and a complete complementary code derived from them are defined and discussed a general method for generating this code is also discussed a synchronous multiple user spread spectrum multiple system is proposed that uses n shift cross orthogonal sequences

the navier stokes limit of the boltzmann equation for bounded collision kernels the present work establishes a navier stokes limit for the boltzmann equation considered over the infinite spatial domain r3 appropriately scaled families of diperna lions renormalized solutions are shown to have fluctuations whose limit points in the w l1 topology are governed by leray solutions of the limiting navier stokes equations this completes the arguments in bardos golse levermore commun pure appl math 46 5 667 753 1993 for the steady case and in lions masmoudi arch ration mech anal 158 3 173 193 2001 for the time dependent case

semi implicit linearized multiple relaxation time formulation of lattice boltzmann schemes for mixture modeling a lattice boltzmann model for mixture modeling is developed by applying the multiple relaxation time mrt approach to the hamel model which allows one to derive from a general framework different model equations independently proposed like the gross krook model and the sirovich model by imposing some physical constraints the mrt lattice boltzmann hamel model reduces to the generalized mrt lattice boltzmann gross krook model involving the local maxwellian centered on the barycentric velocity which allows one to tune independently the species diffusivity the mixture kinematic viscosity and the mixture bulk viscosity reducing the number of moving particles over the total is possible to deal effectively with mass particle ratios far from unity and for this reason to model the pressure driven diffusion a convenient numerical approach is proposed for solving the developed model which essentially widens the stability range of conventional schemes in terms of dimensionless relaxation frequencies by solving explicitly the advection operator together with the nonlinear terms of the collisional operator and solving implicitly the residual linear terms in this way the calculations are drastically reduced and the operative matrices can be computed once for all at the beginning of the calculation implying moderate additional computational demand following this approach a semi implicit linearized backward euler scheme ideal for parallel implementations is proposed in order to achieve the previous results the asymptotic analysis recently suggested for analyzing the macroscopic equations corresponding to lattice boltzmann schemes in the low mach number limit proves to be an effective tool some numerical tests are reported for proving the consistency of the proposed method with both the fick model and maxwell stefan model in the macroscopic limit

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

singular forces and pointlike colloids in lattice boltzmann hydrodynamics we present an accurate method to include arbitrary singular distributions of forces in the lattice boltzmann formulation of hydrodynamics we validate our method with several examples involving stokeslet stresslet and rotlet singularities finding excellent agreement with analytical results a minimal model for sedimenting particles is presented using the method in the dilute limit this model has accuracy comparable to but computational efficiency much greater than algorithms that explicitly resolve the size of the particles

on ternary complementary sequences a pair of real valued sequences a a sub 1 a sub 2 a sub n and b b sub 1 b sub 2 b sub n is called complementary if the sum r spl middot of their autocorrelation functions r sub a spl middot and r sub b spl middot satisfies r spl tau r sub a spl tau r sub b spl tau spl sigma sub i 1 sup n sup spl tau a sub i a sub i spl tau spl sigma sub j 1 sup n spl tau b sub j b sub j spl tau 0 spl forall spl tau spl ne 0 in this paper we introduce a new family of complementary pairs of sequences over the alphabet spl alpha sub 3 1 1 0 the inclusion of zero in the alphabet which may correspond to a pause in transmission leads both to a better understanding of the conventional binary case where the alphabet is spl alpha sub 2 1 1 and to new nontrivial constructions over the ternary alphabet spl alpha sub 3 for every length n we derive restrictions on the location of the zero elements and on the form of the member sequences of the pair we also derive a bound on the minimum number of zeros necessary for the existence of a complementary pair of length n over spl alpha sub 3 the bound is tight as it is met by some of the proposed constructions for infinitely many lengths

a critical analysis of the modified equation technique of warming and hyett abstract warming and hyett developed a modified equation technique in which the behavior of a difference scheme is evaluated by using the coefficients of a certain modified equation specifically they discovered a connection between these coefficients and the multiplication factor obtained from the von neumann analysis since the dissipation and dispersion off error components are determined by the multiplication factor the former properties can be studied using the coefficients of the modified equation the work of warming and hyett represents a key step in the development of the method of modified equations through this work it became clear that modified equations should be derived from the difference scheme rather than from the original differential equation however in order to prove the above connection warming and hyett incorrectly interpreted their modified equations as the actual partial differential equations solved by the difference schemes the main purpose of the current study is to investigate rigorously the above connection without using their interpretation the result of this investigation shows that the above connection is only partially valid for multilevel schemes in the von neumann analysis the multiplication factor associated with a wave number generally has l 1 roots for an l level scheme it is shown that the coefficients of the modified equation provide information for only the principal root

lattice boltzmann model for exterior flows with an annealing preconditioning method in this paper we propose a highly efficient and stable lattice boltzmann method for solving low reynolds number exterior flows using a preconditioning technique the present method is based on replacing the constant preconditioning parameter gamma within uniform grids guo phys rev e 70 066706 2004 by a space and time dependent one in a nested mesh refined domain to do this for the transition from a fine to the neighboring coarser grid gamma has been divided by a factor k which is large initially and anneals stepwise to a small value after some iterations with this technique more than one order of magnitude larger convergence rate can be achieved and several orders of magnitude larger system size can be treated

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

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

a trace identity and its applications to the theory of discrete integrable systems a general theory for studying discrete integrable systems is developed based on a trace identity that the author previously proposed a scheme for generating hierarchies of discrete integrable systems is presented under broad assumptions the resulting hierarchies are shown to consist of liouville integrable hamiltonian systems

discrete adjoint sensitivity analysis for fluid flow topology optimization based on the generalized lattice boltzmann method abstract a discrete adjoint sensitivity analysis for fluid flow topology optimization based on the lattice boltzmann method lbm with multiple relaxation times mrt is developed the lattice boltzmann fluid solver is supplemented by a porosity model using a darcy force the continuous transition from fluid to solid facilitates a gradient based optimization process of the design topology of fluidic channels the adjoint lbm equation which is used to compute the gradient of the optimization objective with respect to the design variables is derived in moment space and found to be as simple as the original lbm the moment based spatial momentum derivatives used to express the discrete objective functional cost function have the advantage that the local stress tensor is a local quantity avoiding the numerical computation of gradients of the discrete velocity field this is particularly useful if dissipation is a design criterion as demonstrated in this paper the method is validated by a detailed comparison with results obtained by borrvall et al for stokes flow while their approach is only valid for stokes flow i e very low reynolds numbers our approach in its present form can in principle be applied for flows of different reynolds numbers just like the navier stokes equation based approaches this point is demonstrated with a bending pipe example for various reynolds numbers

a complete description of golay pairs for lengths up to 100 in his 1961 paper marcel golay showed how the search for pairs of binary sequences of length n with complementary autocorrelation is at worst a 2 6 problem andres in his 1977 master s thesis developed an algorithm which reduced this to a 2 n 2 1 search and investigated lengths up to 58 for existence of pairs in this paper we describe refinements to this algorithm enabling a 2 n 2 5 search at length 82 we find no new pairs at the outstanding lengths 74 and 82 in extending the theory of composition we are able to obtain a closed formula for the number of pairs of length 2 k n generated by a primitive pair of length n combining this with the results of searches at all allowable lengths up to 100 we identify five primitive pairs all others pairs of lengths less than 100 may be derived using the methods outlined

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

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

algebraic structure of discrete zero curvature equations and master symmetries of discrete evolution equations an algebraic structure related to discrete zero curvature equations is established it is used to give an approach for generating master symmetries of the first degree for systems of discrete evolution equations and an answer to why there exist such master symmetries the key of the theory is to generate nonisospectral flows t l l 0 from the discrete spectral problem associated with a given system of discrete evolution equations three examples are given

aperiodic autocorrelation and crosscorrelation of polyphase sequences a detailed analysis of the maximum aperiodic autocorrelation of the original chu sequences equivalently p3 p4 pulse compression codes is presented the result implies the best known upper bound on the minimax aperiodic autocorrelation for polyphase sequences except when the length is very small or a perfect square it is well known that determining the minimax aperiodic correlation for polyphase sequence sets is an intractable task the simplest nontrivial cases for barker and general polyphase sequences are solved for the first time

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

single node second order boundary schemes for the lattice boltzmann method abstract based on our recently developed maxwell iteration for the lattice boltzmann method we propose a class of single node boundary schemes for dirichlet boundary conditions of the navier stokes equations the schemes all have second order accuracy for both straight and curved boundaries the accuracy and stability of two specific schemes are examined through several numerical experiments the results validate the second order accuracy and show that a boundary scheme with a convex combination of distribution functions has better stability

derivation and analysis of lattice boltzmann schemes for the linearized euler equations we derive lattice boltzmann lbm schemes to solve the linearized euler equations in 1d 2d and 3d with the future goal of coupling them to an lbm scheme for navier stokes equations and a finite volume scheme for linearized euler equations the derivation uses the analytical maxwellian in a bgk model in this way we are able to obtain second order schemes in addition we perform an l 2 stability analysis numerical results validate the approach

semidirect sums of lie algebras and discrete integrable couplings a relation between semidirect sums of lie algebras and integrable couplings of lattice equations is established and a practicable way to construct integrable couplings is further proposed an application of the resulting general theory to the generalized toda spectral problem yields two classes of integrable couplings for the generalized toda hierarchy of lattice equations the construction of integrable couplings using semidirect sums of lie algebras provides a good source of information on complete classification of integrable lattice equations

relativistic toda systems we present and study poincare invariant generalizations of the galilei invariant toda systems the classical nonperiodic systems are solved by means of an explicit action angle transformation

solving the fokker planck kinetic equation on a lattice we propose a discrete lattice version of the fokker planck kinetic equation in close analogy with the lattice boltzmann scheme our work extends an earlier one dimensional formulation to arbitrary spatial dimension d a generalized hermite gauss procedure is used to construct a discretized kinetic equation and a chapman enskog expansion is applied to adapt the scheme so as to correctly reproduce the macroscopic continuum equations the linear stability of the algorithm with respect to the finite time step delta t is characterized by the eigenvalues of the collision matrix a heuristic second order algorithm in delta t is applied to investigate the time evolution of the distribution function of simple model systems and compared to known analytical solutions preliminary investigations of sedimenting brownian particles subjected to an orthogonal centrifugal force illustrate the numerical efficiency of the lattice fokker planck algorithm to simulate nontrivial situations interactions between brownian particles may be accounted for by adding a standard bhatnagar gross krook collision operator to the discretized fokker planck kernel

a super discrete variational identity and its application for constructing super discrete hamiltonian systems in the paper a super discrete variational identity on lie super algebras is established first it provides an approach for constructing super discrete hamiltonian structures of super evolution lattice equations with discrete zero curvature representation when the super spectral matrix u is selected appropriately as an application super discrete hamiltonian structures of super toda lattice hierarchy are developed and this method can be used to construct super discrete bi hamiltonian structures of more super discrete integrable evolutive hierarchies super discrete variational identity is devoted to deduce super integrability and solutions of super discrete integrable equations

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

lattice boltzmann simulations on irregular grids introduction of the natrium library the lattice boltzmann method is a modern approach to simulate fluid flow in its original formulation it is restricted to regular grids second order discretizations and a unity cfl number this paper describes our new off lattice boltzmann solver natrium an extensible and parallel c code to perform lattice boltzmann simulations on irregular grids natrium also allows high order spatial discretizations and non unity cfl numbers to be used we demonstrate how these features can efficiently decrease the number of grid points required in a simulation and thus reduce the computational time compared to the standard lattice boltzmann method we detail the implementation of a recently proposed semi lagrangian lattice boltzmann method and prove its efficiency in comparisons to other state of the art off lattice boltzmann schemes

analysis and reduction of the spurious current in a class of multiphase lattice boltzmann models we show that the spurious current present near a curved interface in a class of multiphase lattice boltzmann lb models is due to the insufficient isotropy of the discrete gradient operator a method of obtaining highly isotropic gradient operators on a lattice is given numerical simulations show that both the magnitude and the spatial extent of the spurious current are significantly reduced as gradient operators of increasingly higher order of isotropy is adopted in multiphase lb models

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

a knudsen layer theory for lattice gases abstract a knudsen layer theory is presented for lattice gases with arbitrary boundary conditions analytical results are obtained for two special orientations these exhibit anisotropic knudsen layers provided suitable conditions are satisfied however the standard boundary conditions used in previous simulations are shown to be isotropic the bulk steady state extending everywhere in the gas this theory allows a more accurate localization of the obstacle with respect to the lattice nodes these results are in good agreement with the numerical simulations

incompressible navier stokes and euler limits of the boltzmann equation we consider solutions of the boltzmann equation in a d dimensional torus d 2 3 for macroscopic times t n 1 t 0 when the space variations are on a macroscopic scale x n 1r n 2 x in the unit torus let u x t be for t t0 a smooth solution of the incompressible navier stokes equations ins for n 2 and of the incompressible euler equation ie for n 2 we prove that has solutions for t t0 which are close to o 2 in a suitable norm to the local maxwellian p 2 t d 2 exp v u x t 2 2t with constant density p and temperature t this is a particular case defined by the choice of initial values of the macroscopic variables of a class of such solutions in which the macroscopic variables satisfy more general hydrodynamical equations for n 3 these equations correspond to variable density ie while for n 2 they involve higher order derivatives of the density

an integrable coupling family of the toda lattice systems its bi hamiltonian structure and a related nonisospectral integrable lattice family starting from a four by four matrix spectral problem an integrable coupling family of the toda lattice systems is derived a pair of discrete hamiltonian operators is presented and a sequence of the corresponding hamiltonian functionals is constructed by using the discrete variational identity then the bi hamiltonian structure of the obtained integrable coupling family is established finally a nonisospectral integrable lattice family associated with the obtained integrable coupling family is given through nonisospectral discrete zero curvature representation

generalized lattice boltzmann equation with forcing term for computation of wall bounded turbulent flows in this paper we present a framework based on the generalized lattice boltzmann equation glbe using multiple relaxation times with forcing term for eddy capturing simulation of wall bounded turbulent flows due to its flexibility in using disparate relaxation times the glbe is well suited to maintaining numerical stability on coarser grids and in obtaining improved solution fidelity of near wall turbulent fluctuations the subgrid scale sgs turbulence effects are represented by the standard smagorinsky eddy viscosity model which is modified by using the van driest wall damping function to account for reduction of turbulent length scales near walls in order to be able to simulate a wider class of problems we introduce forcing terms which can represent the effects of general nonuniform forms of forces in the natural moment space of the glbe expressions for the strain rate tensor used in the sgs model are derived in terms of the nonequilibrium moments of the glbe to include such forcing terms which comprise a generalization of those presented in a recent work yu et al comput fluids 35 957 2006 variable resolutions are introduced into this extended glbe framework through a conservative multiblock approach the approach whose optimized implementation is also discussed is assessed for two canonical flow problems bounded by walls viz fully developed turbulent channel flow at a shear or friction reynolds number re of 183 6 based on the channel half width and three dimensional 3d shear driven flows in a cubical cavity at a re of 12 000 based on the side length of the cavity comparisons of detailed computed near wall turbulent flow structure given in terms of various turbulence statistics with available data including those from direct numerical simulations dns and experiments showed good agreement the glbe approach also exhibited markedly better stability characteristics and avoided spurious near wall turbulent fluctuations on coarser grids when compared with the single relaxation time srt based approach moreover its implementation showed excellent parallel scalability on a large parallel cluster with over a thousand processors

boundary forces in lattice boltzmann analysis of momentum exchange algorithm when lattice boltzmann methods are used to simulate fluid structure interaction problems they need to be coupled with additional routines to evaluate the boundary forces without destroying the efficiency and accuracy of the original method we use the asymptotic expansion technique to analyze one such approach the momentum exchange algorithm investigating its properties in detail whether it can be improved and in which cases it can be successfully used a statement regarding the accuracy is presented together with results of numerical tests which illustrate the theoretical considerations

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

a multiplicative decomposition of poiseuille number on rarefaction and roughness by lattice boltzmann simulation poiseuille number of rarefied gas flow in channels with designed roughness is studied and a multiplicative decomposition of poiseuille number on the effects of rarefaction and roughness is proposed the numerical methodology is based on the mesoscopic lattice boltzmann method in order to eliminate the effect of compressibility the incompressible lattice boltzmann model is used and the periodic boundary is imposed on the inlet and outlet of the channel the combined bounced condition is applied to simulate the velocity slip on the wall boundary numerical results reveal the two opposite effects that velocity gradient and friction factor near the wall increase as roughness effect increases meanwhile the increments of the rarefaction effect and velocity slip lead to a corresponding decrement of friction factor an empirical relation of poiseuille number which contains the two opposite effects and has a better physical meaning is proposed in the form of multiplicative decomposition and then is validated by available experimental and numerical results

convergence of lattice boltzmann methods for navier stokes flows in periodic and bounded domains combining an asymptotic analysis of the lattice boltzmann method with a stability estimate we are able to prove some convergence results which establish a strict relation to the incompressible navier stokes equation the proof applies to the lattice boltzmann method in the case of periodic domains and for specific bounded domains if the dirichlet boundary condition is realized with the bounce back rule

unified framework for a side by side comparison of different multicomponent algorithms lattice boltzmann vs phase field model lattice boltzmann models lbm and phase field models pfm are two of the most widespread approaches for the numerical study of multicomponent fluid systems both methods have been successfully employed by several authors but despite their popularity still remains unclear how to properly compare them and how they perform on the same problem here we present a unified framework for the direct one to one comparison of the multicomponent lbm against the pfm we provide analytical guidelines on how to compare the shan chen sc lattice boltzmann model for non ideal multicomponent fluids with a corresponding free energy fe lattice boltzmann model then in order to properly compare the lbm vs the pfm we propose a new formulation for the free energy of the cahn hilliard navier stokes equations finally the lbm model is numerically compared with the corresponding phase field model solved by means of a pseudo spectral algorithm this work constitute a first attempt to set the basis for a quantitative comparison between different algorithms for multicomponent fluids we limit our scope to the few of the most common variants of the two most widespread methodologies namely the lattice boltzmann model sc and fe variants and the phase field model

lattice boltzmann method for 3 d flows with curved boundary in this work we investigate two issues that are important to computational efficiency and reliability in fluid dynamic applications of the lattice boltzmann equation lbe 1 computational stability and accuracy of different lattice boltzmann models and 2 the treatment of the boundary conditions on curved solid boundaries and their 3 d implementations three athermal 3 d lbe models q15d3 q19d3 and q27d3 are studied and compared in terms of efficiency accuracy and robustness the boundary treatment recently developed by filippova and hanel 1998 j comp phys 147 219 and mei et al 1999 j comp phys 155 307 in 2 d is extended to and implemented for 3 d the convergence stability and computational efficiency of the 3 d lbe models with the boundary treatment for curved boundaries were tested in simulations of four 3 d flows 1 fully developed flows in a square duct 2 flow in a 3 d lid driven cavity 3 fully developed flows in a circular pipe and 4 a uniform flow over a sphere we found that while the 15 velocity 3 d q15d3 model is more prone to numerical instability and the q27d3 is more computationally intensive the q19d3 model provides a balance between computational reliability and efficiency through numerical simulations we demonstrated that the boundary treatment for 3 d arbitrary curved geometry has second order accuracy and possesses satisfactory stability characteristics

stability and stabilization of the lattice boltzmann method we revisit the classical stability versus accuracy dilemma for the lattice boltzmann methods lbm our goal is a stable method of second order accuracy for fluid dynamics based on the lattice bhatnager gross krook method lbgk the lbgk scheme can be recognized as a discrete dynamical system generated by free flight and entropic involution in this framework the stability and accuracy analysis are more natural we find the necessary and sufficient conditions for second order accurate fluid dynamics modeling in particular it is proven that in order to guarantee second order accuracy the distribution should belong to a distinguished surface the invariant film up to second order in the time step this surface is the trajectory of the quasi equilibrium distribution surface under free flight the main instability mechanisms are identified the simplest recipes for stabilization add no artificial dissipation up to second order and provide second order accuracy of the method two other prescriptions add some artificial dissipation locally and prevent the system from loss of positivity and local blowup demonstration of the proposed stable lbgk schemes are provided by the numerical simulation of a one dimensional 1d shock tube and the unsteady 2d flow around a square cylinder up to reynolds number mathrm re ensuremath sim 20 phantom rule 0 2em 0ex 000

hamiltonian and quasi hamiltonian structures associated with semi direct sums of lie algebras the trace variational identity is generalized to zero curvature equations associated with non semi simple lie algebras or equivalently lie algebras possessing degenerate killing forms an application of the resulting generalized variational identity to a class of semi direct sums of lie algebras in the akns case furnishes hamiltonian and quasi hamiltonian structures of the associated integrable couplings three examples of integrable couplings for the akns hierarchy are presented one hamiltonian and two quasi hamiltonian

accuracy analysis of high order lattice boltzmann models for rarefied gas flows in this work we have theoretically analyzed and numerically evaluated the accuracy of high order lattice boltzmann lb models for capturing non equilibrium effects in rarefied gas flows in the incompressible limit the lb equation is shown to be able to reduce to the linearized bhatnagar gross krook bgk equation therefore when the same gauss hermite quadrature is used lb method closely resembles the discrete velocity method dvm in addition the order of hermite expansion for the equilibrium distribution function is found not to be directly correlated with the approximation order in terms of the knudsen number to the bgk equation for incompressible flows meanwhile we have numerically evaluated the lb models for a standing shear wave problem which is designed specifically for assessing model accuracy by excluding the influence of gas molecule surface interactions at wall boundaries the numerical simulation results confirm that the high order terms in the discrete equilibrium distribution function play a negligible role in capturing non equilibrium effect for low speed flows by contrast appropriate gauss hermite quadrature has the most significant effect on whether lb models can describe the essential flow physics of rarefied gas accurately our simulation results where the effect of wall gas interactions is excluded can lead to conclusion on the lb modeling capability that the models with higher order quadratures provide more accurate results for the same order gauss hermite quadrature the exact abscissae will also modestly influence numerical accuracy using the same gauss hermite quadrature the numerical results of both lb and dvm methods are in excellent agreement for flows across a broad range of the knudsen numbers which confirms that the lb simulation is similar to the dvm process therefore lb method can offer flexible models suitable for simulating continuum flows at the navier stokes level and rarefied gas flows at the linearized boltzmann model equation level

asymptotic analysis of finite difference methods with this article we want to advocate the use of asymptotic methods for the analysis of finite difference schemes we present several examples to demonstrate the applicability of the approach advantages over the modified equation and truncation error analysis are pointed out

evaluation of the external force term in the discrete boltzmann equation a representation of the forcing term in the boltzmann equation based on a hermite expansion of the boltzmann distribution function in velocity phase space is derived based on this description of the forcing term a systematic comparison of previous lattice boltzmann models describing a nonideal gas behavior is given

a combined lattice bgk level set method for immiscible two phase flows we present a lattice boltzmann method lbm for simulating immiscible multi phase flows which is based on a coupling of lbm with the level set method the computation of immiscible flows using the lbm with bgk collision operator is done separately in each of the fluid domains and coupled at the interface by an appropriate boundary condition in this way we preserve sharp interfaces between different fluid phases we apply a new interface condition that represents the fluid mechanical jump conditions at the interface in the kinetic lbm framework the level set method is applied to compute the evolution of the interface between fluids numerical results demonstrate the applicability of the method even in the presence of large viscosity and density ratios

fluid dynamic limits of kinetic equations i formal derivations the connection between kinetic theory and the macroscopic equations of fluid dynamics is described in particular our results concerning the incompressible navier stokes equations are based on a formal derivation in which limiting moments are carefully balanced rather than on a classical expansion such as those of hilbert or chapman enskog the moment formalism shows that the limit leading to the incompressible navier stokes equations like that leading to the compressible euler equations is a natural one in kinetic theory and is contrasted with the systematics leading to the compressible navier stokes equations some indications of the validity of these limits are given more specifically the connection between the diperna lions renormalized solution of the classical boltzmann equation and the leray solution of the navier stokes equations is discussed

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

connection between kinetic methods for fluid dynamic equations and macroscopic finite difference schemes the lattice boltzmann method lbm for the incompressible navier stokes ns equations and the gas kinetic scheme for the compressible ns equations are based on the kinetic theory of gases in the latter case however it is shown that the kinetic formulation is necessary only in the discontinuous reconstruction of fluid dynamic variables for shock capturing analogously we will discuss the reduction of a kinetic method for the incompressible case where the lbm scheme will be shown to shrink to an artificial compressibility type finite difference scheme we will prove first that a simple and compact lbm scheme cannot catch rarefied effects beyond navier stokes and hence that it is worth the effort to develop kinetic based fd alternatives finally we will propose two improvements to existing kinetic based fd schemes first of all a the proposed scheme is formulated purely in terms of macroscopic quantities on a compact stencil secondly b the semi implicit formulation is proposed in order to increase the stability we think that this work may be useful to others in realizing the actual possibilities of simple lbm schemes beyond navier stokes and in adopting the suggested improvements in their actual fd codes

study of kinetic equation for non ideal gases using lattice boltzmann method interparticle forces from bbgky hierarchy the first equation of the bbgky hierarchy is closed with a truncation scheme which conserves mass momentum and total energy resulting kinetic equation is solved numerically using the lattice boltzmann method over an isothermal d2q9 lattice the inter particle forces are derived using a density gradient approximation to the collision term of the bbgky hierarchy and the resulting non ideal equation of state is calculated in this paper we show analytically that the time rate of change of boltzmann s h function i e frac dh left t right dt is zero for this truncation scheme implying reversibility in time therefore a bgk term is added to the collision integral to describe the macroscopic irreversibility both the local and global h functions are calculated numerically for significant variations in the density we also have simulated a switching experiment over this system and obtained the non equilibrium work distributions

a bbgky based density gradient approximation of interparticle forces application for discrete boltzmann methods abstract the force term accounting for interparticle interactions with application to discrete boltzmann simulation methods is derived using a density gradient expansion of the bbgky collision operator it is shown that previous calculations based on essentially the same mean field theory philosophy do not apply the density gradient approximation in a self consistent fashion thus these previous models have errors in the second virial coefficient as well as coefficients associated with gradient terms in the pressure tensor this new treatment corrects these shortcomings

adiabatic perturbations for compactons under dissipation and numerically induced dissipation compacton propagation under dissipation shows amplitude damping and the generation of tails the numerical simulation of compactons by means of dissipative schemes also show the same behaviors the truncation error terms of a numerical method can be considered as a perturbation of the original partial differential equation and perturbation methods can be applied to its analysis for dissipative schemes or when artificial dissipation is added the adiabatic perturbation method yields evolution equations for the amplitude loss in the numerical solution and the amplitude of the numerically induced tails in this paper such methods are applied to the k 2 2 rosenau hyman equation showing a very good agreement between perturbative and numerical results

new complete complementary codes for peak to mean power control in multi carrier cdma owing to the zero non trivial aperiodic correlation sum properties complete complementary codes ccc have been applied to asynchronous multi carrier code division multiple access mc cdma communications in order to provide zero interference performance when each complementary code is arranged to be a matrix the peak to mean envelope power ratio pmepr of the ccc mc cdma system is determined by the column sequences of the complementary matrices the existing ccc have the column sequence pmepr of m where m denotes the number of subcarriers in a ccc mc cdma system in practice m is generally large and a pmepr approaching this value is unacceptable to solve this problem a new class of ccc using generalized boolean functions and with a column sequence pmepr of at most 2 is proposed in this paper

a systematic framework for the construction of optimal complete complementary codes the complete complementary code ccc that was proposed by suehiro and hatori is a sequence family that is a set of sequence sets with ideal correlation sums numerous studies in the literature show its applications to direct spread code division multiple access ds cdma systems for interchannel interference ici free communication with improved spectral efficiency in this paper we propose a systematic framework for the construction of cccs based on n shift cross orthogonal sequence families n co sfs we show theoretical bounds on the size of n co sfs and cccs and give a set of four algorithms for their generation and extension the algorithms are optimal in the sense that the size of the resultant sequence families achieves theoretical bounds and with the algorithms we can construct an optimal ccc consisting of sequences whose lengths are not only almost arbitrary but even variable between sequence sets we also discuss the family size alphabet size and length of constructible cccs based on the proposed algorithms

computation of gas solid flows by finite difference boltzmann equation abstract in this paper we will discuss in detail how to use a finite difference lattice boltzmann equation model in which an external force term is involved to simulate two way coupling gas solid flows the numerical results are found to be in good agreement with analytical data and some other numerical results

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

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

optimal preconditioning of lattice boltzmann methods a preconditioning technique to accelerate the simulation of steady state problems using the single relaxation time srt lattice boltzmann lb method was first proposed by guo et al z guo t zhao y shi preconditioned lattice boltzmann method for steady flows phys rev e 70 2004 066706 1 the key idea in this preconditioner is to modify the equilibrium distribution function in such a way that by means of a chapman enskog expansion a time derivative preconditioner of the navier stokes ns equations is obtained in the present contribution the optimal values for the free parameter c of this preconditioner are searched both numerically and theoretically the later with the aid of linear stability analysis and with the condition number of the system of ns equations the influence of the collision operator single versus multiple relaxation times mrt is also studied three steady state laminar test cases are used for validation namely the two dimensional lid driven cavity a two dimensional microchannel and the three dimensional backward facing step finally guidelines are suggested for an a priori definition of optimal preconditioning parameters as a function of the reynolds and mach numbers the new optimally preconditioned mrt method derived is shown to improve simultaneously the rate of convergence the stability and the accuracy of the lattice boltzmann simulations when compared to the non preconditioned methods and to the optimally preconditioned srt one additionally direct time derivative preconditioning of the lb equation is also studied

synthesis of power efficient multitone signals with flat amplitude spectrum it is shown that generally any binary or polyphase sequence belonging to a pair of complementary sequences can be used to construct the initial phases of tones forming a multitone signal with the crest factor less than or equal to 6 db the previously proposed shapiro rudin sequences are representatives of a much larger family of binary golay complementary sequences numerical investigations show that the values of the crest factors obtained by applying complementary sequences binary or polyphase are between 5 and 6 db regardless of the number of tones

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

a consistent grid coupling method for lattice boltzmann schemes a method of coupling grids of different mesh size is developed for classical lattice boltzmann lb algorithms on uniform grids the approach is based on an asymptotic analysis revealing suitable quantities equalized along the grid interfaces for exchanging information between the subgrids in contrast to other couplings the method works without overlap zones moreover the grid velocity mach number is not kept constant as the time step depends not linearly but quadratically on the grid spacing to illustrate the basic idea we use a simple lb algorithm solving the advection diffusion equation the proposed grid coupling is validated by numerical convergence studies indicating that the coupling does not affect the second order convergence behavior of the lb algorithm which is observed on uniform grids in order to demonstrate its principal applicability to other lb models the coupling is generalized to the standard d2p9 model for navier stokes flow and tested numerically as we use analytic tools different from the chapman enskog expansion the theoretical background material is given in two appendices in particular the results of numerical experiments are confirmed with a consistency analysis

complementary set matrices satisfying a column correlation constraint motivated by the problem of reducing the peak to average power ratio papr of transmitted signals we consider a design of complementary set matrices whose column sequences satisfy a correlation constraint the design algorithm recursively builds a collection of 2t 1 mutually orthogonal mo complementary set matrices starting from a companion pair of sequences we relate correlation properties of column sequences to that of the companion pair and illustrate how to select an appropriate companion pair to ensure that a given column correlation constraint is satisfied for t 0 companion pair properties directly determine matrix column correlation properties the proposed companion pair based design can construct binary complementary sets with either a minimum out of phase autocorrelation magnitude or a minimum sum of out of phase autocorrelation magnitude for column sequences of length at least up to 28 for t ges 1 reducing correlation merits of the companion pair may lead to improved column correlation properties exhaustive search for companion pairs satisfying a column correlation constraint is infeasible for medium length and long sequences we instead search for two shorter length sequences by minimizing a cost function in terms of their autocorrelation and cross correlation merits in addition by exploiting the well known welch bound sufficient conditions for the existence of companion pairs which satisfy a set of column correlation constraints are given