discrete effects on boundary conditions for the lattice boltzmann equation in simulating microscale gas flows the lattice boltzmann equation lbe has shown its promise in the simulation of microscale gas flows one of the critical issues with this advanced method is to specify suitable slip boundary conditions to ensure simulation accuracy in this paper we study two widely used kinetic boundary conditions in the lbe the combination of the bounce back and specular reflection scheme and the discrete maxwell s scheme we show that i both schemes are virtually equivalent in principle and ii there exist discrete effects in both schemes a strategy is then proposed to adjust the parameters in the two kinetic boundary conditions such that an accurate slip boundary condition can be implemented the numerical results demonstrate that the corrected boundary conditions are robust and reliable

least squares based lattice boltzmann method a meshless approach for simulation of flows with complex geometry a version of lattice boltzmann method lbm is presented in this work which is derived from the standard lbm by using taylor series expansion and optimized by the least squares method the method is basically meshless and can be applied to any complex geometry and nonuniform grids it can also be applied to different lattice models the proposed method explicitly updates the distribution functions at mesh points by an algebraic formulation in which the relevant coefficients are precomputed from the coordinates of mesh points we have successfully applied this method to simulate many two dimensional incompressible viscous flows the numerical results are very accurate and the computational time needed is much less as compared with other existing methods in this paper we mainly show the method

numerical stability of explicit off lattice boltzmann schemes the off lattice boltzmann olb method consists of numerical schemes which are used to solve the discrete boltzmann equation unlike the commonly used lattice boltzmann method the spatial and time steps are uncoupled in the olb method in the currently proposed schemes which can be broadly classified into runge kutta based and characteristics based the size of the time step is limited due to numerical stability constraints in this work we systematically compare the numerical stability of the proposed schemes in terms of the maximum stable time step in line with the overall lb method we investigate the available schemes where the advection approximation is explicit and the collision approximation is either explicit or implicit the comparison is done by implementing these schemes on benchmark incompressible flow problems such as taylor vortex flow poiseuille flow and lid driven cavity flow it is found that the characteristics based olb schemes are numerically more stable than the runge kutta based schemes additionally we have observed that with respect to time step size the scheme proposed by bardow et al 2006 1 is the most numerically stable and computationally efficient scheme compared to similar schemes for the flow problems tested here

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

semi lagrangian schemes for the vlasov equation on an unstructured mesh of phase space a new scheme for solving the vlasov equation using an unstructured mesh for the phase space is proposed the algorithm is based on the semi lagrangian method which exploits the fact that the distribution function is constant along the characteristic curves we use different local interpolation operators to reconstruct the distribution function f some of which need the knowledge of the gradient of f we can use limiter coefficients to maintain the positivity and the l bound of f and optimize these coefficients to ensure the conservation of the l1 norm that is to say the mass by solving a linear programming problem several numerical results are presented in two and three axisymmetric case dimensional phase space the local interpolation technique is well suited for parallel computation

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

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

semi lagrangian implicit bhatnagar gross krook collision model for the finite volume discrete boltzmann method in order to increase the accuracy of temporal solutions reduce the computational cost of time marching and improve the stability associated with collisions for the finite volume discrete boltzmann method an advanced implicit bhatnagar gross krook bgk collision model using a semi lagrangian approach is proposed in this paper unlike existing models in which the implicit bgk collision is resolved either by a temporal extrapolation or by a variable transformation the proposed model removes the implicitness by tracing the particle distribution functions pdfs back in time along their characteristic paths during the collision process an interpolation scheme is needed to evaluate the pdfs at the traced back locations by using the first order interpolation the resulting model allows for the straightforward replacement of f eq n 1 by f eq n no matter where it appears after comparing the proposed model with the existing models under different numerical conditions e g different flux schemes and time marching schemes and using the proposed model to successfully modify the variable transformation technique three conclusions can be drawn first the proposed model can improve the accuracy by almost an order of magnitude second it can slightly reduce the computational cost therefore the proposed scheme improves accuracy without extra cost finally the proposed model can significantly improve the t limit compared to the temporal interpolation model while having the same t limit as the variable transformation approach the proposed scheme with a second order interpolation is also developed and tested however that technique displays no advantage over the simple first order interpolation approach both numerical and theoretical analyses are also provided to explain why the developed implicit scheme with simple first order interpolation can outperform the same scheme with second order interpolation as well as the existing temporal extrapolation and variable transformation schemes

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

efficient multiple range random walk algorithm to calculate the density of states we present a new monte carlo algorithm that produces results of high accuracy with reduced simulational effort independent random walks are performed concurrently or serially in different restricted ranges of energy and the resultant density of states is modified continuously to produce locally flat histograms this method permits us to directly access the free energy and entropy is independent of temperature and is efficient for the study of both 1st order and 2nd order phase transitions it should also be useful for the study of complex systems with a rough energy landscape

finite element lattice boltzmann simulations of free surface flow in a concentric cylinder the annular centrifugal contactor is a compact mixer centrifuge device designed for liquid liquid extraction operations in processes for recycling nuclear fuel the flow in the annulus of a centrifugal contactor is similar to the taylor vortex flow with superimposed axial flow the major differences are that the contactor has one end that is open to air and the free surface effects dominate the annular flow in this study we demonstrate the application of a finite element lattice boltzmann equation fe lbe method to the annular mixing geometry as found in a centrifugal contactor the computational results are validated with available experimental observations with the reynolds number re in the range of 1250

compression quality prediction model for jpeg2000 a compression quality prediction model is proposed for grey images coding with jpeg2000 with this model the compression quality psnr could be estimated according to the given compression ratio cr and the image activity measures iam without coding images the image activity measure is the weighted sum of the iam values based on the 1 pixel distance and 2 pixel distance gradients along horizontal and vertical directions we have shown that iam is a function of the image variance and autocorrelation coefficients based on shannon s rate distortion theorem a theoretical justification is provided for the correlation of iam with psnr experimental results show that the prediction error is lower than 1 db for more than 70 sample images when cr is higher than 15 the prediction error is less than 2 db for over 90 images this prediction performance is acceptable for general applications

lattice boltzmann method on unstructured grids further developments we discuss further developments of the finite volume lattice boltzmann formulation on unstructured grids it is shown that the method tolerates significant grid distortions without showing any appreciable numerical viscosity effects at second order in the mesh size a theoretical argument of plausibility for such a property is presented in addition a set of boundary conditions which permit to handle flows with open boundaries is also introduced and numerically demonstrated for the case of channel flows and driven cavity flows

consistent second order boundary implementations for convection diffusion lattice boltzmann method in this study an alternative second order boundary scheme is proposed under the framework of the convection diffusion lattice boltzmann lb method for both straight and curved geometries with the proposed scheme boundary implementations are developed for the dirichlet neumann and linear robin conditions in a consistent way the chapman enskog analysis and the hermite polynomial expansion technique are first applied to derive the explicit expression for the general distribution function with second order accuracy then the macroscopic variables involved in the expression for the distribution function is determined by the prescribed macroscopic constraints and the known distribution functions after streaming see the paragraph after eq 29 for the discussions of the streaming step in lb method after that the unknown distribution functions are obtained from the derived macroscopic information at the boundary nodes for straight boundaries boundary nodes are directly placed at the physical boundary surface and the present scheme is applied directly when extending the present scheme to curved geometries a local curvilinear coordinate system and first order taylor expansion are introduced to relate the macroscopic variables at the boundary nodes to the physical constraints at the curved boundary surface in essence the unknown distribution functions at the boundary node are derived from the known distribution functions at the same node in accordance with the macroscopic boundary conditions at the surface therefore the advantages of the present boundary implementations are i the locality i e no information from neighboring fluid nodes is required ii the consistency i e the physical boundary constraints are directly applied when determining the macroscopic variables at the boundary nodes thus the three kinds of conditions are realized in a consistent way it should be noted that the present focus is on two dimensional cases and theoretical derivations as well as the numerical validations are performed in the framework of the two dimensional five velocity lattice model

discrete unified gas kinetic scheme for all knudsen number flows low speed isothermal case based on the boltzmann bgk bhatnagar gross krook equation in this paper a discrete unified gas kinetic scheme dugks is developed for low speed isothermal flows the dugks is a finite volume scheme with the discretization of particle velocity space after the introduction of two auxiliary distribution functions with the inclusion of collision effect the dugks becomes a fully explicit scheme for the update of distribution function furthermore the scheme is an asymptotic preserving method where the time step is only determined by the courant friedricks lewy condition in the continuum limit numerical results demonstrate that accurate solutions in both continuum and rarefied flow regimes can be obtained from the current dugks the comparison between the dugks and the well defined lattice boltzmann equation method d2q9 is presented as well

simulating fluid flow over sinusoidal surfaces using the lattice boltzmann method the objective of this paper is to analyze the laminar flow of a newtonian fluid pressurized and sheared through a two dimensional channel with one sinusoidal wall the motivation of this work is the investigation of shear flows in lubrication the effects of reynolds number and the geometrical dimensions on the velocity distributions and on the flow factors are studied numerically using the lattice boltzmann method lbm the results are verified with analytical and other numerical solutions

optimal pruning with applications to tree structured source coding and modeling an algorithm introduced by l breiman et al 1984 in the context of classification and regression trees is reinterpreted and extended to cover a variety of applications in source coding and modeling in which trees are involved these include variable rate and minimum entropy tree structured vector quantization minimum expected cost decision trees variable order markov modeling optimum bit allocation and computer graphics and image processing using quadtrees a concentration on the first of these and a detailed analysis of variable rate tree structured vector quantization are provided it is found that variable rate tree structured vector quantization outperforms not only the fixed rate variety but also full search vector quantization the successive approximation character of variable rate tree structured vector quantization permits it to degrade gracefully if the rate is reduced at the encoder this has applications to the problem of buffer overflow

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

taylor series expansion and least squares based lattice boltzmann method two dimensional formulation and its applications an explicit lattice boltzmann method lbm is developed in this paper to simulate flows in an arbitrary geometry the method is based on the standard lbm taylor series expansion and the least squares approach the final formulation is an algebraic form and essentially has no limitation on the mesh structure and lattice model theoretical analysis for the one dimensional 1d case showed that the version of the lbm could recover the navier stokes equations with second order accuracy a generalized hydrodynamic analysis is conducted to study the wave number dependence of shear viscosity for the method numerical simulations of the 2d lid driven flow in a square cavity and a polar cavity flow as well as the no flow simulation in a square cavity have been carried out favorable results were obtained and compared well with available data in the literature indicating that the present method has good prospects in practical applications

high order finite elements applied to the discrete boltzmann equation a discontinuous galerkin approach for solving the discrete boltzmann equation is presented allowing to compute approximate solutions for fluid flow problems based on a two dimensional high order finite element and an explicit euler time stepping scheme the d2q9 model is discretized and the results are compared to the exact solution of the navier stokes equation four numerical examples are considered including stationary and instationary problems with curved boundaries it is demonstrated that the proposed method allows to obtain the desired highly efficient exponential convergence copyright 2006 john wiley sons ltd

a bit allocation method based on picture activity for still image coding bit allocation or the quantizer assignment problem is a basic and essential issue in lossy picture coding the optimal solution for the bit allocation problem can be found by the lagrangian method however it requires much computational time and memory to reduce complexity overhead we propose a fast scheme using a picture activity measure comparison among the existing activity measurement methods is presented to select the most reliable activity measure and the mapping relation between the activity value and a quantization parameter is proposed

entropic lattice boltzmann method for turbulent flow simulations boundary conditions abstract we introduce a new concept of boundary conditions for realization of the lattice boltzmann simulations of turbulent flows the key innovation is the use of a universal distribution function for particles analogous to the tamm mott smith solution for the shock wave in the classical boltzmann kinetic equation turbulent channel flow simulations demonstrate that the new boundary enables accurate results even with severely under resolved grids generalization to complex boundary is illustrated with an example of turbulent flow past a circular cylinder

analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice boltzmann bgk model in this paper we analytically solve the velocity of the lattice boltzmann bgk equation lbgk for several simple flows the analysis provides a framework to theoretically analyze various boundary conditions in particular the analysis is used to derive the slip velocities generated by various schemes for the nonslip boundary condition we find that the slip velocity is zero as long as f e 0 at boundaries no matter what combination of distributions is chosen the schemes proposed by nobleet al and by inamuroet al yield the correct zeroslip velocity while some other schemes such as the bounce back scheme and the equilibrium distribution scheme would inevitably generate a nonzero slip velocity the bounce back scheme with the wall located halfway between a flow node and a bounce back node is also studied for the simple flows considered and is shown to produce results of second order accuracy the momentum exchange at boundaries seems to be highly related to the slip velocity at boundaries to be specific the slip velocity is zero only when the momentum dissipated by boundaries is equal to the stress provided by fluids

implementation of a high order compact finite difference lattice boltzmann method in generalized curvilinear coordinates abstract in this work the implementation of a high order compact finite difference lattice boltzmann method cfdlbm is performed in the generalized curvilinear coordinates to improve the computational efficiency of the solution algorithm to handle curved geometries with non uniform grids the incompressible form of the discrete boltzmann equation with the bhatnagar gross krook bgk approximation with the pressure as the independent dynamic variable is transformed into the generalized curvilinear coordinates herein the spatial derivatives in the resulting lattice boltzmann lb equation in the computational plane are discretized by using the fourth order compact finite difference scheme and the temporal term is discretized with the fourth order runge kutta scheme to provide an accurate and efficient incompressible flow solver a high order spectral type low pass compact filter is used to regularize the numerical solution and remove spurious waves generated by boundary conditions flow non linearities and grid non uniformity all boundary conditions are implemented based on the solution of governing equations in the generalized curvilinear coordinates the accuracy and efficiency of the solution methodology presented are demonstrated by computing different benchmark steady and unsteady incompressible flow problems a sensitivity study is also conducted to evaluate the effects of grid size and filtering on the accuracy and convergence rate of the solution four test cases considered herein for validating the present computations and demonstrating the accuracy and robustness of the solution algorithm are unsteady couette flow and steady flow in a 2 d cavity with non uniform grid and steady and unsteady flows over a circular cylinder and the naca0012 hydrofoil at different flow conditions results obtained for the above test cases are in good agreement with the existing numerical and experimental results the study shows the present solution methodology based on the implementation of the high order compact finite difference lattice boltzmann method cfdlbm in the generalized curvilinear coordinates is robust efficient and accurate for solving steady and unsteady incompressible flows over practical geometries

discrete unified gas kinetic scheme for all knudsen number flows ii thermal compressible case this paper is a continuation of our work on the development of multiscale numerical scheme from low speed isothermal flow to compressible flows at high mach numbers in our earlier work z l guo et al phys rev e 88 033305 2013 a discrete unified gas kinetic scheme dugks was developed for low speed flows in which the mach number is small so that the flow is nearly incompressible in the current work we extend the scheme to compressible flows with the inclusion of thermal effect and shock discontinuity based on the gas kinetic shakhov model this method is an explicit finite volume scheme with the coupling of particle transport and collision in the flux evaluation at a cell interface as a result the time step of the method is not limited by the particle collision time with the variation of the ratio between the time step and particle collision time the scheme is an asymptotic preserving ap method where both the chapman enskog expansion for the navier stokes solution in the continuum regime and the free transport mechanism in the rarefied limit can be precisely recovered with a second order accuracy in both space and time the dugks is an idealized multiscale method for all knudsen number flow simulations a number of numerical tests including the shock structure problem the sod tube problem in a whole range of degree of rarefaction and the two dimensional riemann problem in both continuum and rarefied regimes are performed to validate the scheme comparisons with the results of direct simulation monte carlo dsmc and other benchmark data demonstrate that the dugks is a reliable and efficient method for multiscale flow problems

optimal trellis based buffered compression and fast approximations the authors formalize the description of the buffer constrained adaptive quantization problem for a given set of admissible quantizers used to code a discrete nonstationary signal sequence in a buffer constrained environment they formulate the optimal solution they also develop slightly suboptimal but much faster approximations these solutions are valid for any globally minimum distortion criterion which is additive over the individual elements of the sequence as a first step they define the problem as one of constrained discrete optimization and establish its equivalence to some of the problems studied in the field of integer programming forward dynamic programming using the viterbi algorithm is shown to provide a way of computing the optimal solution then they provide a heuristic algorithm based on lagrangian optimization using an operational rate distortion framework that with computing complexity reduced by an order of magnitude approaches the optimally achievable performance the algorithms can serve as a benchmark for assessing the performance of buffer control strategies and are useful for applications such as multimedia workstation displays video encoding for cd roms and buffered jpeg coding environments where processing delay is not a concern but decoding buffer size has to be minimized

spectral element discontinuous galerkin lattice boltzmann simulation of flow past two cylinders in tandem with an exponential time integrator in this paper a spectral element discontinuous galerkin sedg lattice boltzmann discretization and an exponential time marching scheme are used to study the flow field past two circular cylinders in tandem arrangement the basic idea is to discretize the streaming step of the lattice boltzmann equation by using the sedg method to get a system of ordinary differential equations odes whose exact solutions are expressed by using a large matrix exponential the approximate solution of the resulting odes are obtained from a projection method based on a krylov subspace approximation this approach allows us to approximate the matrix exponential of a very large and sparse matrix by using a matrix of much smaller dimension the exponential time integration scheme is useful especially when computations are carried out at high courant friedrichs lewy cfl numbers where most explicit time marching schemes are inaccurate simulations of flow were carried out for a circular cylinder at re 20 and for two circular cylinders in tandem at re 40 and a spacing of 2 5d where d is the diameter of the cylinders we compare our results with those from a fourth order runge kutta scheme that is restricted by the cfl number in addition important flow parameters such as the drag coefficients of the two cylinders and the wake length behind the rear cylinder were calculated by using the exponential time integration scheme these results are compared with results from our simulation using the rk scheme and with existing benchmark results

chebyshev collocation spectral lattice boltzmann method for simulation of low speed flows in this study the chebyshev collocation spectral lattice boltzmann method ccslbm is developed and assessed for the computation of low speed flows both steady and unsteady flows are considered here the discrete boltzmann equation with the bhatnagar gross krook approximation based on the pressure distribution function is considered and the space discretization is performed by the chebyshev collocation spectral method to achieve a highly accurate flow solver to provide accurate unsteady solutions the time integration of the temporal term in the lattice boltzmann equation is made by the fourth order runge kutta scheme to achieve numerical stability and accuracy physical boundary conditions based on the spectral solution of the governing equations implemented on the boundaries are used an iterative procedure is applied to provide consistent initial conditions for the distribution function and the pressure field for the simulation of unsteady flows the main advantage of using the ccslbm over other high order accurate lattice boltzmann method lbm based flow solvers is the decay of the error at exponential rather than at polynomial rates note also that the ccslbm applied does not need any numerical dissipation or filtering for the solution to be stable leading to highly accurate solutions three two dimensional 2d test cases are simulated herein that are a regularized cavity the taylor vortex problem and doubly periodic shear layers the results obtained for these test cases are thoroughly compared with the analytical and available numerical results and show excellent agreement the computational efficiency of the proposed solution methodology based on the ccslbm is also examined by comparison with those of the standard streaming collision classical lbm and two finite difference lbm solvers the study indicates that the ccslbm provides more accurate and efficient solutions than these lbm solvers in terms of cpu and memory usage and an exponential convergence is achieved rather than polynomial rates the solution methodology proposed the ccslbm is also extended to three dimensions and a 3d regularized cavity is simulated the corresponding results are presented and validated indications are that the ccslbm developed and applied herein is robust efficient and accurate for computing 2d and 3d low speed flows note also that high accuracy solutions obtained by applying the ccslbm can be used as benchmark solutions for the assessment of other lbm based flow solvers

an eulerian description of the streaming process in the lattice boltzmann equation this paper presents a novel strategy for solving discrete boltzmann equation dbe for simulation of fluid flows this strategy splits the solution procedure into streaming and collision steps as in the lattice boltzmann equation lbe method the streaming step can then be carried out by solving pure linear advection equations in an eulerian framework this offers two significant advantages over previous methods first the relationship between the relaxation parameter and the discretization of the collision term developed from the lbe method is directly applicable to the dbe method the resulting dbe collision step remains local and poses no constraint on time step second decoupling of the advection step from the collision step facilitates implicit discretization of the advection equation on arbitrary meshes an implicit unstructured dbe method is constructed based on this strategy and is evaluated using several test cases of flow over a backward facing step lid driven cavity flow and flow past a circular cylinder the speedup of convergence for some cases improves by a factor of about 20

truncation error analysis of lattice boltzmann methods a truncation error analysis is performed for models based on the lattice boltzmann lb equation this analysis involves two steps the recursive application of the lb equation and a taylor series expansion unlike previous analytical studies of lb methods the present work does not assume an asymptotic relationship between the temporal and spatial discretization parameters or between the probability distribution function f and its equilibrium distribution feq effective finite difference stencils are derived for both the distribution function and the primitive variables i e density and velocity the governing partial differential equations are also recovered the associated truncation errors are derived and the results are validated by numerical simulation of analytic flows analysis of the truncation errors elucidates the roles of the kinetic theory relaxation parameter and the discretization parameters x and t the effects of initial and boundary conditions are also addressed and are shown to significantly affect the overall accuracy of the method

some progress in lattice boltzmann method part i nonuniform mesh grids a new lattice boltzmann algorithm is proposed to simulate the navier stokes equation on arbitrary nonuniform mesh grids the new algorithm retains the advantages of the lattice boltzmann method parallel of algorithm ease of programming and ability to incorporate microscopic interactions a simulation of flow in a two dimensional symmetric channel with sudden expansion is carried out using the new algorithm on a nonuniform mesh the results of the simulation are in excellent agreement with previous experimental and numerical results

analysis and assessment of the no slip and slip boundary conditions for the discrete unified gas kinetic scheme the discrete unified gas kinetic scheme dugks with a force term is a finite volume solver for the boltzmann equation unlike the standard lattice boltzmann method lbm dugks can be applied on nonuniform grids for both the lbm and dugks the boundary conditions need to be processed through the density distribution function so researchers introduced the boundary conditions from the lbm frame into the dugks however the accuracy of these boundary conditions in the dugks has not been studied thoroughly through strict theoretical deduction we find that the bounce back bb scheme leads to a different dependence of the numerical error term in the dugks as compared to the lbm the error term is influenced by the relaxation time and the body force and it can be reduced by lowering the kinetic viscosity unlike the bb scheme the nonequilibrium bounce back scheme has the ability to implement real no slip boundary condition furthermore two slip boundary conditions incorporated with navier s slip model are introduced from the lbm framework into the dugks the tangential momentum change based tmac scheme can be used directly in the dugks because it generates no numerical error term in the dugks for the combination of the bounce back and specular reflection schemes bsr the relation between the slip length and the combination parameter should be modified in accordance with the numerical error term analysis shows that the tmac scheme can simulate a wider range of slip length than the bsr scheme numerical simulations of the couette flow and the poiseuille flow confirm our theoretical analysis

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

a spectral difference lattice boltzmann method for solution of inviscid compressible flows on structured grids in this work a spectral difference lattice boltzmann method sdlbm is developed and applied for an accurate simulation of two dimensional inviscid compressible flows on structured grids the compressible form of the discrete boltzmann bgk equation is used in which multiple particle speeds have to be employed to correctly model the compressibility in a thermal fluid here the 2d compressible lattice boltzmann lb model proposed by watari is applied the spectral difference sd method is implemented for the solution of the lb equation in which the particle distribution function is stored at the solution points while the fluxes are computed at the flux points for calculating the particle distribution function for time accurate solutions the fourth order runge kutta scheme is used to discretize the temporal term in the lb equation note that the procedure of implementing the sd method to solve the lb equation is nearly the same as that procedure developed in the literature for the solution of the euler equations the accuracy and robustness of the present solution methodology are demonstrated by simulating different benchmark compressible flow problems a sensitivity study is also conducted to evaluate the effects of the numerical parameters and the grid size distribution on the accuracy and performance of the solution at first three inviscid compressible flow problems namely the stationary isentropic vortex the shock tube and the shock vortex interaction are solved by using the sdlbm to demonstrate the accuracy and robustness of the present solution methodology results computed for these test cases are in good agreement with the analytical and the available numerical solutions to more assess the accuracy and robustness of the sdlbm a third order finite volume lbm fvlbm is also developed and the solutions obtained by these two methods for the test cases simulated are thoroughly compared with each other it is demonstrated that the sdlbm is more accurate and robust compressible inviscid flow solver that can be used for evaluating the other compressible lb based flow solvers as the final problem the supersonic flow past a bump is simulated to demonstrate the accuracy and robustness of the sdlbm in reaching to a steady state solution

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

the lattice boltzmann equation on irregular lattices a general framework to extend the lattice boltzmann equation to arbitrary lattice geometries is presented and numerically demonstrated for the case of a two dimensional poiseuille flow the new scheme considerably extends the range of applicability of the boltzmann method to problems requiring the use of nonuniform grids

a spectral element discontinuous galerkin lattice boltzmann method for nearly incompressible flows we present a spectral element discontinuous galerkin lattice boltzmann method for solving nearly incompressible flows decoupling the collision step from the streaming step offers numerical stability at high reynolds numbers in the streaming step we employ high order spectral element discontinuous galerkin discretizations using a tensor product basis of one dimensional lagrange interpolation polynomials based on gauss lobatto legendre grids our scheme is cost effective with a fully diagonal mass matrix advancing time integration with the fourth order runge kutta method we present a consistent treatment for imposing boundary conditions with a numerical flux in the discontinuous galerkin approach we show convergence studies for couette flows and demonstrate two benchmark cases with lid driven cavity flows for re 400 5000 and flows around an impulsively started cylinder for re 550 9500 computational results are compared with those of other theoretical and computational work that used a multigrid method a vortex method and a spectral element model

three ways to lattice boltzmann a unified time marching picture it is shown that the lattice boltzmann equation lbe corresponds to an explicit verlet time marching scheme for a continuum generalized boltzmann equation with a memory delay equal to a half time step this proves second order accuracy of lbe with respect to this generalized equation with no need of resorting to any implicit time marching procedure crank nicholson and associated nonlinear variable transformations it is also shown and numerically demonstrated that this equivalence is not only formal but it also translates into a complete equivalence of the corresponding computational schemes with respect to the hydrodynamic equations second order accuracy with respect to the continuum kinetic equation is also numerically demonstrated for the case of the taylor green vortex it is pointed out that the equivalence is however broken for the case in which mass and or momentum are not conserved such as for chemically reactive flows and mixtures for such flows the time centered implicit formulation may indeed offer a better numerical accuracy

semi lagrangian off lattice boltzmann method for weakly compressible flows the lattice boltzmann method is a simulation technique in computational fluid dynamics in its standard formulation it is restricted to regular computation grids second order spatial accuracy and a unity courant friedrichs lewy cfl number this paper advances the standard lattice boltzmann method by introducing a semi lagrangian streaming step the proposed method allows significantly larger time steps unstructured grids and higher order accurate representations of the solution to be used the appealing properties of the approach are demonstrated in simulations of a two dimensional taylor green vortex doubly periodic shear layers and a three dimensional taylor green vortex

lattice boltzmann modeling of microchannel flow in slip flow regime we present the lattice boltzmann equation lbe with multiple relaxation times mrt to simulate pressure driven gaseous flow in a long microchannel we obtain analytic solutions of the mrt lbe with various boundary conditions for the incompressible poiseuille flow with its walls aligned with a lattice axis the analytical solutions are used to realize the dirichlet boundary conditions in the lbe we use the first order slip boundary conditions at the walls and consistent pressure boundary conditions at both ends of the long microchannel we validate the lbe results using the compressible navier stokes ns equations with a first order slip velocity the information preservation direct simulation monte carlo ip dsmc and dsmc methods as expected the lbe results agree very well with ip dsmc and dsmc results in the slip velocity regime but deviate significantly from ip dsmc and dsmc results in the transition flow regime in part due to the inadequacy of the slip velocity model while still agreeing very well with the slip ns results possible extensions of the lbe for transition flows are discussed

best wavelet packet bases in a rate distortion sense a fast rate distortion r d optimal scheme for coding adaptive trees whose individual nodes spawn descendents forming a disjoint and complete basis cover for the space spanned by their parent nodes is presented the scheme guarantees operation on the convex hull of the operational r d curve and uses a fast dynamic programing pruning algorithm to markedly reduce computational complexity applications for this coding technique include r coefman et al s yale univ 1990 generalized multiresolution wavelet packet decomposition iterative subband coders and quadtree structures applications to image processing involving wavelet packets as well as discrete cosine transform dct quadtrees are presented

on the finite difference based lattice boltzmann method in curvilinear coordinates the lattice boltzmann method is a microscopic based approach for solving the fluid flow problems at the macroscopic scales the presently popular method uses regularly spaced lattices and cannot handle curved boundaries with desirable flexibility to circumvent such difficulties a finite difference based lattice boltzmann method fdlbm in curvilinear coordinates is explored using body fitted coordinates with non uniform grids several test cases including the impulsively started cylindrical couette flow steady state cylindrical couette flow steady flow over flat plates and steady flow over a circular cylinder are used to examine various issues related to the fdlbm the effect of boundary conditions for the distribution functions on the solution the merits between second order central difference and upwind schemes for advection terms and the effect of the reynolds number are investigated favorable results are obtained using fdlbm in curvilinear coordinates indicating that the method is potentially capable of solving finite reynolds number flow problems in complex geometries

polydisperse chains placed on a one dimensional lattice abstract using a transfer matrix technique we calculate the entropy of polydisperse chains placed on an one dimensional lattice as a function of the density of internal and endpoint monomers the polydispersivity is determined considering different activities for the two types of monomers as is usual for equilibrium polymerization and living polymers if the mean number of monomers in the chains is fixed the entropy as a function of the density of monomers displays a maximum and is limited from below by the entropy of monodisperse chains the increase of entropy due to the polydispersivity is a linear function of the density of monomers we also calculate the distribution of chain sizes obtaining an exponential relation

on overflow and underflow problems in buffer instrumented variable length coding of fixed rate memoryless sources corresp it is well known that variable length coding schemes can be employed in entropy encoding of finite alphabet sources to transmit these codes over a synchronous channel however requires a buffer since in practice this buffer is of finite size it is subject to both overflow and undertow the buffer behavior is studied with particular application to huffman coding of the outputs of an optimum uniform threshold quantizer driven by a memoryless gaussian source fairly general upper and lower bounds on the average terminal time are developed under certain conditions the tightness of these bounds is verified and asymptotic formulas are developed as an example an encoding scheme employing huffman codes in conjunction with uniform quantization of memoryless gaussian sources is considered and the buffer behavior as a function of the buffer size and output rate is studied

explicit finite difference lattice boltzmann method for curvilinear coordinates in this paper a finite difference based lattice boltzmann method for curvilinear coordinates is proposed in order to improve the computational efficiency and numerical stability of a recent method r mei and w shyy j comput phys 143 426 1998 in which the collision term of the boltzmann bhatnagar gross krook equation for discrete velocities is treated implicitly in the present method the implicitness of the numerical scheme is removed by introducing a distribution function different from that being used currently as a result an explicit finite difference lattice boltzmann method for curvilinear coordinates is obtained the scheme is applied to a two dimensional poiseuille flow an unsteady couette flow a lid driven cavity flow and a steady flow around a circular cylinder the numerical results are in good agreement with the results of previous studies extensions to other lattice boltzmann models based on nonuniform meshes are also discussed

a characteristic galerkin method for discrete boltzmann equation abstract the characteristic galerkin finite element method for the discrete boltzmann equation is presented to simulate fluid flows in complex geometries the inherent geometric flexibility of the finite element method permits the easy use of simple cartesian variables on unstructured meshes and the mesh clustering near large gradients the characteristic galerkin procedure with appropriate boundary condition results in accurate solutions with little numerical diffusion several test cases are conducted including unsteady couette flows lid driven cavity flows and steady flow past a circular cylinder on unstructured meshes the numerical results are in good agreement with previous analytical if applicable numerical and experimental results

numerical simulation of sound generation in a mixing layer by the finite difference lattice boltzmann method we simulated aerodynamic sound in a two dimensional mixing layer using the finite difference lattice boltzmann method fdlbm we introduced a finite difference scheme called the dispersion relation preserving drp scheme into the fdlbm to carry out an accurate simulation of aerodynamic problems the scheme is designed such that the dispersion relation of the finite difference scheme is the same as that of the original partial differential equations and is useful for acoustic simulations a turbulent flow field was simulated by large eddy simulation les using the smagorinsky model and the results were compared with those from a direct simulation based on the navier stokes equations to confirm the usefulness of this method the combination of the fdlbm and the drp scheme was shown to be very effective for direct simulations of aerodynamic sound

entropy of dimers chains placed on a one dimensional lattice with q states abstract we calculate the entropy of a chain of dimers placed on a one dimensional lattice as a function of the density of monomers we consider n p dimer chains with a number of monomers m 2 which may assume q states orientations on the one dimensional lattice in this work we treated a simple model which has exact solutions both in the micro canonical and grand canonical formalisms the analytic result in the micro canonical and grand canonical ensembles were successfully confirmed by a monte carlo algorithm

lattice boltzmann method on irregular meshes a finite volume scheme for the lattice boltzmann method fvlbm is described the scheme uses a finite volume formulation based on triangular elements in two dimensions and is implemented assuming that velocity space is isotropically discretized at each node in position space the accuracy of the finite volume scheme is numerically demonstrated by comparing the computed macroscopic velocity field with the exact solution of the navier stokes equations for the flow of an incompressible fluid between two relatively rotating cylinders the fvlbm scheme is applicable to irregular two dimensional regions which contain both exterior and interior boundaries of arbitrary shape thus the range of applicability of systems to which the fvlbm may be applied is seen to be significantly extended

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

least squares finite element scheme for the lattice boltzmann method on an unstructured mesh a numerical model of the lattice boltzmann method lbm utilizing least squares finite element method in space and the crank nicolson method in time is developed this method is able to solve fluid flow in domains that contain complex or irregular geometric boundaries by using the flexibility and numerical stability of a finite element method while employing accurate least squares optimization fourth order accuracy in space and second order accuracy in time are derived for a pure advection equation on a uniform mesh while high stability is implied from a von neumann linearized stability analysis implemented on unstructured mesh through an innovative element by element approach the proposed method requires fewer grid points and less memory compared to traditional lbm accurate numerical results are presented through two dimensional incompressible poiseuille flow couette flow and flow past a circular cylinder finally the proposed method is applied to estimate the permeability of a randomly generated porous media which further demonstrates its inherent geometric flexibility

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

trellis coded quantization of memoryless and gauss markov sources trellis coded quantization tcq is developed and applied to the encoding of memoryless and gauss markov sources the theoretical justification for the approach is alphabet constrained rate distortion theory which is a dual to the channel capacity argument that motivates trellis coded modulation tcm the authors adopt the notions of signal set expansion set partitioning and branch labeling of tcm but modify the techniques to account for the source distribution to design tcq coders of low complexity with excellent mean squared error mse performance for a memoryless uniform source tcq provides an mse within 0 21 db of the distortion rate bound at all positive integral rates the performance is superior to that promised by the coefficient of quantization for all of the best lattices known in dimensions 24 or less for a memoryless gaussian source the tcq performance at rates of 0 5 1 and 2 b sample is superior to all previous results the authors found in the literature the encoding complexity of tcq is very modest tcq is incorporated into a predictive coding structure for the encoding of gauss markov sources simulation results for first second and third order gauss markov sources are presented

least squares finite element lattice boltzmann method a new numerical model of the lattice boltzmann method utilizing least squares finite element in space and crank nicolson method in time is presented the new method is able to solve problem domains that contain complex or irregular geometric boundaries by using finite element method s geometric flexibility and numerical stability while employing efficient and accurate least squares optimization for the pure advection equation on a uniform mesh the proposed method provides for fourth order accuracy in space and second order accuracy in time with unconditional stability in the time domain accurate numerical results are presented through two dimensional incompressible poiseuille flow and couette flow

performance evaluation of the general characteristics based off lattice boltzmann scheme and dugks for low speed continuum flows the general characteristics based off lattice boltzmann scheme proposed by bardow et al 1 hereafter bardow s scheme and the discrete unified gas kinetic scheme dugks 2 are two methods that successfully overcome the time step restriction by the collision time which is commonly seen in many other kinetic schemes in this work we first perform a theoretical analysis of the two schemes in the finite volume framework by comparing their numerical flux evaluations it is found that the effect of collision term is considered in the evaluation of the cell interface distribution function in both schemes which explains why they can overcome the time step restriction and can give accurate results even as the time step is much larger than the collision time the difference between the two schemes lies in the treatment of the integral of the collision term when evaluating the cell interface distribution function in which bardow s scheme uses the rectangular rule while dugks uses the trapezoidal rule the performance of the two schemes i e accuracy stability and efficiency are then compared by simulating several two dimensional flows including the unsteady taylorgreen vortex flow the steady lid driven cavity flow and the laminar boundary layer problem it is observed that dugks can give more accurate results than bardow s scheme with a same mesh size furthermore the numerical stability of bardow s scheme decreases as the courantfriedrichslewy cfl number approaches to 1 while the stability of dugks is not affected by the cfl number apparently as long as cfl 1 it is also observed that dugks is twice as expensive as the bardow s scheme with the same mesh size

finite volume lattice boltzmann method we present a finite volume formulation for the lattice boltzmann method fvlbm based on standard bilinear quadrilateral elements in two dimensions the accuracy of this scheme is demonstrated by comparing the velocity field with the analytical solution of the navier stokes equations for time dependent rotating couette flow and taylor vortex flow to demonstrate the flexibility of the scheme we have also simulated a modified rotating couette flow where the inner cylinder has an elliptical shape the results agree with those obtained from the traditional marker and cell method the fvlbm scheme is applicable to arbitrarily shaped two dimensional regions and thus the range of applicability of the lattice boltzmann method has been significantly extended

finite volume scheme for the lattice boltzmann method on unstructured meshes department of mathematics and statistics bowling green state university bowling green ohio 43403 received 9 september 1998 a nite volume scheme for the lattice boltzmann method is developed for unstructured triangular meshes intwo dimensions the accuracy of this new scheme is demonstrated by comparing the numerical results with theexact solutions to the navier stokes equations for taylor vortex ow shear ow between two parallel plates shear ow between two rotating cylinders and poiseuille ow the agreement between the numerical andanalytical results is very good for each of these tests s1063 651x 99 07804 6 pacs number s 47 10 1g 47 11 1j 05 20 ddi introduction