the convergence of the perturbed newton method and its application for ill conditioned problems abstract iterative methods such as newton s behave poorly when solving ill conditioned problems they become slow first order and decrease their accuracy in this paper we analyze deeply and widely the convergence of a modified newton method which we call perturbed newton in order to overcome the usual disadvantages newton s one presents the basic point of this method is the dependence of a parameter affording a degree of freedom that introduces regularization choices for that parameter are proposed the theoretical analysis will be illustrated through examples

a solution algorithm for the fluid dynamic equations based on a stochastic model for molecular motion in this paper a stochastic model is presented to simulate the flow of gases which are not in thermodynamic equilibrium like in rarefied or micro situations for the interaction of a particle with others statistical moments of the local ensemble have to be evaluated but unlike in molecular dynamics simulations or dsmc no collisions between computational particles are considered in addition a novel integration technique allows for time steps independent of the stochastic time scale the stochastic model represents a fokker planck equation in the kinetic description which can be viewed as an approximation to the boltzmann equation this allows for a rigorous investigation of the relation between the new model and classical fluid and kinetic equations the fluid dynamic equations of navier stokes and fourier are fully recovered for small relaxation times while for larger values the new model extents into the kinetic regime numerical studies demonstrate that the stochastic model is consistent with navier stokes in that limit but also that the results become significantly different if the conditions for equilibrium are invalid the application to the knudsen paradox demonstrates the correctness and relevance of this development and comparisons with existing kinetic equations and standard solution algorithms reveal its advantages moreover results of a test case with geometrically complex boundaries are presented

a one parameter family of quadratically convergent iteration formulae a new one parameter family of iteration methods for solving nonlinear equations is presented the convergence analysis shows that their order of convergence is two numerical examples are given to illustrate the efficiency and performance of the proposed methods

finite volume approximation of two phase fluid flows based on an approximate roe type riemann solver abstract we introduce an approximate roe type riemann solver for the numerical simulation of two phase fluid flows composed of liquid droplets suspended in gas we compute a roe linearization of some well conditioned approximate rankine hugoniot relations in non conservation form the computed solutions are found to be in good agreement with the exact solution in one dimension slab geometry we extend this solver to two dimensional geometries using a finite volume formulation

a lattice boltzmann model for the simulation of fluid flow the authors set out the theory for a lattice boltzmann algorithm capable of mimicking the navier stokes equation for fluid flow in two dimensions 2d the solution satisfies criteria of galilean invariance and isotropy and viscosity is obtained by direct reference to the viscous term in the navier stokes equation it is possible to specify directly the viscosity and other hydrodynamic parameters without reference to specific collision modes the model was tested by simulating 2d flow through a plane channel poiseuille flow a parabolic flow profile was obtained in excellent agreement with the analytical navier stokes solution they conclude that the algorithm can be used to model 2d fluid flow

on a class of quadratic convergence iteration formulae without derivatives a class of iterative formulae without derivatives are proposed in this paper these methods are shown to be quadratic convergence some numerical tests are given

lattice boltzmann schemes for the nonlinear schrodinger equation the lattice boltzmann lb method is applied to solve the time dependent nonlinear schr odinger nls equation through approximating the reaction term at different orders of accuracy three diffusion reaction lb schemes are constructed for the cubic nls equation a lb initial condition is proposed to include the first order nonequilibrium distribution function these lb schemes are used to solve the one soliton propagation and the homoclinic orbit problems detailed simulation results confirm that the high order reaction term and the lb initial condition are effective in reducing the truncation errors compared with the crank nicolson finite difference scheme the lb scheme is found to give at least comparable and generally more accurate approximation for the cubic nls equation

three dimensional unsaturated flow modeling using cellular automata 1 the parabolic partial differential equation describing fluid flow in partially saturated porous media richards equation is highly nonlinear due to pressure head dependencies in the specific soil moisture capacity and relative hydraulic conductivity terms in order to solve richards equation several numerical techniques have been developed which starting from the discretization of the partial differential equation produced even more accurate models leading to complex and computationally expensive simulations for large scale systems a three dimensional unsaturated flow modeling developed through a simulation environment based on cellular automata ca is described in this paper the proposed model represents an extension of the original computational paradigm of cellular automata because it uses a macroscopic ca approach where local laws with a clear physical meaning govern interactions among automata this ca structure aimed at simulating a large scale system is based on functionalities capable of increasing its computational capacity both in terms of working environment and in terms of the optimal number of processors available for parallel computing the model has been validated with reference multidimensional solutions taken from benchmarks in literature showing a good agreement even in the cases where nonlinearity is very marked furthermore some analyses have been carried out considering quantization techniques aimed at transforming the ca model into an asynchronous structure the use of these techniques in a three dimensional benchmark allowed a considerable reduction in the number of local interactions among adjacent automata without changing the efficiency of the model especially when simulations are characterized by scarce mass exchanges finally from a computational point of view the higher efficiency values were achieved running the model on a parallel architecture obtaining a high speedup very close to the optimal with the maximum number of processors available

an improved lattice boltzmann method for simulating advective diffusive processes in fluids abstract lattice boltzmann methods are widely used to simulate advective diffusive processes in fluids lattice bhatnagar gross krook methods presented in the literature mostly just exhibit first order spatial accuracy and introduce errors proportional to the velocity squared formulations proposed to alleviate this have only been partly successful and are valid only in certain specific situations we present and demonstrate here a formulation that produces no such second order errors this formulation suggests that a subtle but important adjustment is all it takes to improve the accuracy of the method the key to the improved accuracy of this new model is the non standard definition of the concentration that relates to the distribution function describing the advection diffusion in lattice boltzmann the main advantage of the algorithm comes to view when simulating situations where fluid density variations appear the present formulation of the advection diffusion algorithm will by taking into account these fluid density variations drastically reduce the errors produced compared to the standard formulations we also show how a source term is included in this new formulation without it losing its second order spatial accuracy

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

discrete lattice effects on the forcing term in the lattice boltzmann method we show that discrete lattice effects must be considered in the introduction of a force into the lattice boltzmann equation a representation of the forcing term is then proposed with the representation the navier stokes equation is derived from the lattice boltzmann equation through the chapman enskog expansion several other existing force treatments are also examined

cellular automaton fluids a model for flow in porous media numerical models of fluid flow through porous media can be developed from either microscopic or macroscopic properties the large scale viewpoint is perhaps the most prevalent darcy s law relates the chief macroscopic parameters of interest flow rate permeability viscosity and pressure gradient and may be invoked to solve for any of these parameters when the others are known in practical situations however this solution may not be possible attention is then typically focused on the estimation of permeability and numerous numerical methods based on knowledge of the microscopic pore space geometry have been proposed because the intrinsic inhomogeneity of porous media makes the application of proper boundary conditions difficult microscopic flow calculations have typically been achieved with idealized arrays of geometrically simple pores throats and cracks i propose here an attractive alternative which can freely and accurately model fluid flow in grossly irregular geometries this new method s

a new scheme for source term in lbgk model for convection diffusion equation a new scheme for source term in the lattice bgk lbgk model for convection diffusion equation is proposed unlike the models proposed previously the present scheme only requires the source term in order of the knudsen number by adding a differential operator of the source term to the evolution equation the scheme can be applied to reaction diffusion systems directly numerical results are found to be in excellent agreement with the analytical solutions it is also found that the numerical accuracy of the present scheme is generally much better than that of the existing models

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

a hybrid multi time step framework for pore scale and continuum scale modeling of solute transport in porous media abstract in this paper we propose a computational framework which is based on a domain decomposition technique to employ both finite element method which is a popular continuum modeling approach and lattice boltzmann method which is a popular pore scale modeling approach in the same computational domain to bridge the gap across the disparate length and time scales we first propose a new method to enforce continuum scale boundary conditions i e dirichlet and neumann boundary conditions onto the numerical solution from the lattice boltzmann method this method is based on maximization of entropy and preserve the non negativity of discrete distributions under the lattice boltzmann method the proposed computational framework allows different grid sizes orders of interpolation and time steps in different subdomains this allows for different desired resolutions in the numerical solution in different subdomains through numerical experiments the effect of grid and time step refinement disparity of time steps in different subdomains domain partitioning and the number of iteration steps on the accuracy and rate of convergence of the proposed methodology are studied finally to showcase the performance of this framework in porous media applications we use it to simulate the dissolution of calcium carbonate in a porous structure

a one parameter family of second order iteration methods a new one parameter family of iteration methods for finding simple roots of nonlinear equations is developed error analysis providing the second order convergence is given numerical experience shows that the method is comparable to the well known newton s method

traveling waves solution of convection diffusion systems whose convection terms are weakly nonconservative application to the modeling of two phase fluid flows the paper is concerned with the derivation of explicit approximate jump conditions for the shock waves solutions of hyperbolic systems in nonconservation form extracted from a known second order convection diffusion system the shock waves are defined as the limit as the diffusion tends to zero of the traveling waves solution of the second order system although no explicit jump conditions may be found for general hyperbolic systems in nonconservation form we derive an asymptotic expansion of the nonexplicit jump relations in the case of two phase fluid flows we indeed observe that the terms in nonconservation form arise from pressure gradient forces which act on droplets and are small in the sense that the a small number appears in front of them we obtain an asymptotic expansion of the nonexplicit jump relations whose first two terms can be computed explicitly

heat transfer in lattice bgk modeled fluid the thermal lattice bgk model is a recently suggested numerical tool aiming at solving problems of thermohydrodynamics the quality of the lattice bgk simulation is checked in this paper by calculating temperature profiles in the couette flow under different eckert and mach numbers a revised lower order model is proposed to improve the accuracy and the higher order model is proved to be advantageous in this respect especially in the flow regime with a higher mach number

hyperbolic two pressure models for two phase flow abstract for some time it has been known that many of the two phase flow models lead to ill posed cauchy problems because they have complex characteristic values a necessary condition at least in the linear case for the cauchy problem to be well posed is that it be stable in the sense of von neumann for systems of partial differential equations of first order stability in the sense of von neumann is essentially equivalent to the condition that the model be hyperbolic all real characteristic values and complete set of characteristic vectors herein models are developed which have real characteristic values for all physically acceptable states state space and except for a set of measure zero have a complete set of characteristic vectors in state space therefore these models are hyperbolic a e almost everywhere in state space also they are stable in the sense of von neumann a e in state space even without inclusion of viscosity terms the models discussed herein are developed for the case of two phase separated planar flow and include transverse momentum considerations these models are referred to as two pressure models because each phase is assumed to exist at an average pressure different from the average pressure in the other phase the pressure fields are related through momentum considerations numerical results on a steady state problem show good agreement with existing steady state results numerical results on a transient problem agree with a single pressure model until the onset of numerical instability in the single pressure model compared to the single pressure hydrostatic model the two pressure model approximates additional physical features and is shown to be a viable approach for the case of separated flow

boltzmann cellular automata studies of the spinodal decomposition abstract a nonlinear galilean invariant 2 color boltzmann cellular automaton is used to study spinodal decomposition in 2 dimensional systems the initial conditions for the process correspond to a well mixed state of two fluids present in equal proportions we specify two types of such initial conditions corresponding to a correlated quench and to a deep quench in the former case a specific color is assigned randomly to each site in the latter individual states on each site are populated by the two colors about evenly with small fluctuations in the correlated quench situation the domain growth exponent is initially equal to 0 33 0 06 and for the late time stage it is equal to 0 66 0 06 in the deep quench situation on the other hand the effective exponent from initial value of 0 33 takes on the value of 0 82 0 05 for intermediate time scales and only at later times it crosses over to the exponent corresponding to the correlated quench spinodal decomposition taking place in a porous medium is slower and the effective exponents are nonuniversal inadequacies in the existing models of the surface tension in cellular automata are pointed out

simulations of complex fluids by mixed lattice boltzmann finite difference methods abstract we present the numerical results of simulations of complex fluids under shear flow we employ a mixed approach which combines the lattice boltzmann method for solving the navier stokes equation and a finite difference scheme for the convection diffusion equation the evolution in time of shear banding phenomenon is studied this is allowed by the presented numerical model which takes into account the evolution of local structures and their effect on fluid flow

nonequilibrium scheme for computing the flux of the convection diffusion equation in the framework of the lattice boltzmann method in this paper we propose a local nonequilibrium scheme for computing the flux of the convection diffusion equation with a source term in the framework of the multiple relaxation time mrt lattice boltzmann method lbm both the chapman enskog analysis and the numerical results show that at the diffusive scaling the present nonequilibrium scheme has a second order convergence rate in space a comparison between the nonequilibriumschemeandtheconventionalsecond ordercentral differenceschemeindicatesthat althoughboth schemes have a second order convergence rate in space the present nonequilibrium scheme is more accurate than thecentral differencescheme inaddition thefluxcomputationrenderedbythepresentschemealsopreservesthe parallel computation feature of the lbm making the scheme more efficient than conventional finite difference schemes in the study of large scale problems finally a comparison between the single relaxation time model and the mrt model is also conducted and the results show that the mrt model is more accurate than the single relaxation time model both in solving the convection diffusion equation and in computing the flux

a method for near equilibrium discrete velocity gas flows we present a simulation scheme for discrete velocity gases based on local thermodynamic equilibrium exploting the kinetic nature of discrete velocity gases in that context results in a natural splitting of fluxes and the resultant scheme strongly resembles the original process the kinetic nature of the scheme and the modeling of the infinite collision rate limit result in a small value of the coefficient of numerical viscosity the behavior of which is remarkably physical a first order method and two second order methods using the total variation diminishing principle are developed and an example application is presented given the same computer resources it is expected that with this approach a much higher reynold s number will be achievable than presently possible with either lattice gas automata or lattice boltzmann approaches the ideas being general the scheme is applicable to any discrete velocity model and to lattice gases as well

lattice boltzmann equation calculation of internal pressure driven turbulent flow we describe a mixing length extension of the lattice boltzmann approach to the simulation of an incompressible liquid in turbulent flow the method uses a simple adaptable closure algorithm to bound the lattice boltzmann fluid incorporating a law of the wall the test application of an internal pressure driven and smooth duct flow recovers correct velocity profiles for reynolds number to 1 25 105 in addition the reynolds number dependence of the friction factor in the smooth wall branch of the moody chart is correctly recovered the method promises a straightforward extension to other curves of the moody chart and to cylindrical pipe flow

an improved bounce back scheme for complex boundary conditions in lattice boltzmann method in recent years the lattice boltzmann method lbm has been widely adopted to simulate various fluid systems and the boundary treatment has been an active topic during the lbm development in this paper we present a novel approach to improve the bounce back boundary treatment for moving surfaces with arbitrary configurations we follow the framework originally proposed by ladd a j c ladd numerical simulations of particulate suspensions via a discretized boltzman equation part 1 theoretical foundation journal of fluid mechanics 271 1994 285 309 however the adjustment in the density distribution during the bouncing back process at the boundary is calculated using the midpoint velocity inter extrapolated from the boundary and fluid velocities instead of the real boundary velocity in the ladd method this modification ensures that the bouncing back process and the density distribution adjustment both take place at a same location the midpoint of a boundary lattice link and thus removes the discrepancy of bouncing back at the midpoint but density distribution adjustment at the boundary point in the original ladd method when compared with other existing boundary models this method involves a simpler algorithm and exhibits a comparable or even better accuracy in describing flow field and flow structure interaction as demonstrated by several test simulations therefore this boundary method could be considered as a competitive alternative for boundary treatment in lbm simulations especially for particulate and porous flows with large fluid solid interfacial areas

study of the 1d lattice boltzmann shallow water equation and its coupling to build a canal network the d1q3 lattice boltzmann lb shallow water equation is analyzed in detail and compared with other numerical schemes analytical results are derived and used to discuss the accuracy and stability of the model we show how such d1q3 lb models for canal reaches may be easily coupled with various hydraulic interconnection structures to build models of complex irrigation networks

new high order convergence iteration methods without employing derivatives for solving nonlinear equations abstract a family of new iteration methods without employing derivatives is proposed in this paper we have proved that these new methods are quadratic convergence their efficiency is demonstrated by numerical experiments the numerical experiments show that our algorithms are comparable to well known methods of newton and steffensen furthermore combining the new method with bisection method we construct another new high order iteration method with nice asymptotic convergence properties of the diameters b n a n

initial and boundary conditions for the lattice boltzmann method an alternative approach of implementing initial and boundary conditions for the lattice boltzmann method is presented the basic idea is to calculate the lattice boltzmann populations at a boundary node from the fluid variables that are specified at this node using the gradients of the fluid velocity the numerical performance of the lattice boltzmann method is tested on several problems with exact solutions and is also compared to an explicit finite difference projection method the discretization error of the lattice boltzmann method decreases quadratically with finer resolution both in space and in time the roundoff error of the lattice boltzmann method creates problems unless double precision arithmetic is used

nonlinear stability of compressible thermal lattice bgk models the nonlinear stability of thermal lattice bgk models is examined by means of computer simulation for the case of one and two dimensional compressible flows it is shown that in one dimension 1d the method is stable on a sizeable range of flow speeds and temperatures in two dimensions 2d the method is stable even in the presence of negative distribution functions but on a smaller stability domain the computational efficiency of the method compares favorably with classical algorithms for compressible flows such as the lambda scheme and the lax wendroff scheme

lattice boltzmann method for diffusion limited partial dissolution of fluids a lattice boltzmann model for two partially miscible fluids is developed by partially miscible we mean that although there is a definite interfacial region separating the two fluids with a surface tension force acting at all points of the transition region each fluid can nonetheless accept molecules from the other fluid up to a set solubility limit we allow each fluid to diffuse into the other with the solubility and diffusivity in each fluid being input parameters the approach is to define two regions within the fluid one interfacial region having finite width across which most of the concentration change occurs and in which a surface tension force and color separation step are allowed for and one miscible fluid region where the concentration of the binary fluids follows an advection diffusion equation and the mixture as a whole obeys the navier stokes incompressible flow equations numerical examples are presented in which the algorithm produces results that are quantitatively compared to exact analytical results as well as qualitatively examined for their reasonableness the model has the ability to simulate how bubbles of one fluid flow through another while dissolving their contents as well as to simulate a range of practical invasion problems such as injecting supercritical co 2 into a porous material saturated with water for sequestration purposes

the lattice boltzmann equation a new tool for computational fluid dynamics abstract we present a series of applications which demonstrate that the lattice boltzmann equation is an adequate computational tool to address problems spanning a wide spectrum of fluid regimes ranging from laminar to fully turbulent flows in two and three dimensions

interpolation methods and the accuracy of lattice boltzmann mesh refinement a lattice boltzmann model to solve the equivalent of the navier stokes equations on adaptively refined grids is presented a method for transferring information across interfaces between different grid resolutions was developed following established techniques for finite volume representations this new approach relies on a space time interpolation and solving constrained least squares problems to ensure conservation the effectiveness of this method at maintaining the second order accuracy of lattice boltzmann is demonstrated through a series of benchmark simulations and detailed mesh refinement studies these results exhibit smaller solution errors and improved convergence when compared with similar approaches relying only on spatial interpolation examples highlighting the mesh adaptivity of this method are also provided

a new continuation newton like method and its deformation this paper presents a family of new continuation newton like methods and its deformations for computing approximate solutions of the non linear algebraic equation f x 0 from a practical point of view the new methods are vast superior

phase separation of incompressible binary fluids with lattice boltzmann methods we introduce new versions of lattice boltzmann methods lbm for incompressible binary mixtures where fluctuations of total density are inhibited as a test for the improved algorithms we consider the problem of phase separation of two dimensional binary mixtures quenched from a disordered state into the coexistence region we find that the stability properties of lbm are greatly improved the control of density fluctuations and the possibility of running longer simulations allow a more precise evaluation of the growth exponent

numerical study of the ordering properties of lamellar phase the quench of a binary mixture into a stable lamellar phase is numerically investigated we present a novel approach to study the phenomenological equations governing the system dynamics basedon the combination of lattice boltzmann and1nite d equations we can access large systems on time scales long enough to 1nd evidence of dynamical scaling regime in the ordering process when hydrodynamics is operating c

an improved immersed boundary lattice boltzmann method for simulating three dimensional incompressible flows the recently proposed boundary condition enforced immersed boundary lattice boltzmann method ib lbm 14 is improved in this work to simulate three dimensional incompressible viscous flows in the conventional ib lbm the restoring force is pre calculated and the non slip boundary condition is not enforced as compared to body fitted solvers as a result there is a flow penetration to the solid boundary this drawback was removed by the new version of ib lbm 14 in which the restoring force is considered as unknown and is determined in such a way that the non slip boundary condition is enforced since eulerian points are also defined inside the solid boundary the computational domain is usually regular and the cartesian mesh is used on the other hand to well capture the boundary layer and in the meantime to save the computational effort we often use non uniform mesh in ib lbm applications in our previous two dimensional simulations 14 the taylor series expansion and least squares based lattice boltzmann method tllbm was used on the non uniform cartesian mesh to get the flow field the final expression of tllbm is an algebraic formulation with some weighting coefficients these coefficients could be computed in advance and stored for the following computations however this way may become impractical for 3d cases as the memory requirement often exceeds the machine capacity the other way is to calculate the coefficients at every time step as a result extra time is consumed significantly to overcome this drawback in this study we propose a more efficient approach to solve lattice boltzmann equation on the non uniform cartesian mesh as compared to tllbm the proposed approach needs much less computational time and virtual storage its good accuracy and efficiency are well demonstrated by its application to simulate the 3d lid driven cubic cavity flow to valid the combination of proposed approach with the new version of ibm 14 for 3d flows with curved boundaries the flows over a sphere and torus are simulated the obtained numerical results compare very well with available data in the literature

regular article an accurate curved boundary treatment in the lattice boltzmann method the lattice boltzmann equation lbe is an alternative kinetic method capable of solving hydrodynamics for various systems major advantages of the method are due to the fact that the solution for the particle distribution functions is explicit easy to implement and natural to parallelize because the method often uses uniform regular cartesian lattices in space curved boundaries are often approximated by a series of stairs that leads to reduction in computational accuracy in this work a second order accurate treatment of the boundary condition in the lbe method is developed for a curved boundary the proposed treatment of the curved boundaries is an improvement of a scheme due to o filippova and d hanel 1998 j comput phys 147 219 the proposed treatment for curved boundaries is tested against several flow problems 2 d channel flows with constant and oscillating pressure gradients for which analytic solutions are known flow due to an impulsively started wall lid driven square cavity flow and uniform flow over a column of circular cylinders the second order accuracy is observed with a solid boundary arbitrarily placed between lattice nodes the proposed boundary condition has well behaved stability characteristics when the relaxation time is close to 1 2 the zero limit of viscosity the improvement can make a substantial contribution toward simulating practical fluid flow problems using the lattice boltzmann method

numerical study of lattice boltzmann methods for a convection diffusion equation coupled with navier stokes equations numerous lattice boltzmann lb methods have been proposed for solution of the convection diffusion equations cde for the 2d problem d2q9 d2q5 or d2q4 velocity models are usually used when lb convection diffusion models are used to solve a cde coupled with navier stokes equations boundary conditions are found to be critically important for accurately solving the coupled simulations following the idea of a regularized scheme latt et al 2008 phys rev e 77 056703 a regularized boundary condition for solving a cde is proposed a simple extrapolation scheme is also proposed for the neumann boundary condition spatial accuracies of three existing and the proposed boundary conditions are discussed in details the numerical evaluations are based on simulations of steady and unsteady natural convection flows in a cavity and an unsteady taylor couette flow our studies show that the simplest d2q4 model with terms of o u in the equilibrium distribution function is capable of obtaining results of equal accuracy as d2q5 or d2q9 models for the cde a slightly revised lb equation for solving a cde that is used to cancel some unwanted terms does not seem to be necessary for incompressible flows the regularized boundary condition for solving the cde has second order spatial accuracy and it is the best one in terms of the spatial accuracy the regularized scheme and non equilibrium extrapolation scheme are applicable to handle both the dirichlet and neumann boundary conditions for the neumann boundary condition with zero flux all the five boundary conditions are applicable to give accurate results and the bounce back scheme is the simplest one

stable viscosity matrices for systems of conservation laws abstract a natural class of appropriate viscosity matrices for strictly hyperbolic systems of conservation laws in one space dimension u 1 f u x 0 u r m is studied these matrices are admissible in the sense that small amplitude shock wave solutions of the hyperbolic system are shown to be limits of smooth traveling wave solutions of the parabolic system u t f u x v du x x as ifv 0 if d is in this class the class is determined by a linearized stability requirement the cauchy problem for the equation u 1 f u 0 u x vdu xx should be well posed in l 2 uniformly in v as v 0 previous examples of inadmissible viscosity matrices are accounted for through violation of the stability criterion

on a class of quadratically convergent iteration formulae in this paper a new class of iterative formulae having quadratic convergence is presented furthermore these algorithms are comparable to the well known method of newton and the computed results support this theory

a reaction flow lattice boltzmann model the authors describe a development of a lattice boltzmann fluid flow model enabling the simulation of the reaction and flow of low concentration species in two dimensions in principle any number of species and reactions can be implemented in this model in making this development they derive an expression for the solution of the diffusion equation using the lattice boltzmann approach

lattice boltzmann computational fluid dynamics in three dimensions the recent development of the lattice gas method and its extension to the lattice boltzmann method have provided new computational schemes for fluid dynamics both methods are fully paralleled and can easily model many different physical problems including flows with complicated boundary conditions in this paper basic principles of a lattice boltzmann computational method are described and applied to several three dimensional benchmark problems in most previous lattice gas and lattice boltzmann methods a face centered hyper cubic lattice in four dimensional space was used to obtain an isotropic stress tensor to conserve computer memory we develop a model which requires 14 moving directions instead of the usual 24 directions lattice boltzmann models describing two phase fluid flows and magnetohydrodynamics can be developed based on this simpler 14 directional lattice comparisons between three dimensional spectral code results and results using our method are given for simple periodic geometries an important property of the lattice boltzmann method is that simulations for flow in simple and complex geometries have the same speed and efficiency while all other methods including the spectral method are unable to model complicated geometries efficiently

cellular automaton fluids 1 basic theory continuum equations are derived for the large scale behavior of a class of cellular automaton models for fluids the cellular automata are discrete analogues of molecular dynamics in which particles with discrete velocities populate the links of a fixed array of sites kinetic equations for microscopic particle distributions are constructed hydrodynamic equations are then derived using the chapman enskog expansion slightly modified navier stokes equations are obtained in two and three dimensions with certain lattices viscosities and other transport coefficients are calculated using the boltzmann transport equation approximation some corrections to the equations of motion for cellular automaton fluids beyond the navier stokes order are given

computational time and domain size analysis of porous media flows using the lattice boltzmann method the purpose of this study is to investigate the computational time required to describe the fluid flow behavior through a porous medium and its relation to the corresponding domain size the fluid flow behavior is recovered using the lattice boltzmann method lbm the selected methodology has been applied because of its feasibility for mimicking the fluid flow behavior in complex geometries and moving boundaries in this study three different porosities are selected to calculate for several sizes domain the required computational time to reach the steady state two different cases are implemented 1 increasing the transversal area but keeping the layer thickness as a constant and 2 increasing the total volume of the pore domain by increasing all the dimensions of the volume equally the porous media are digitally generated by placing the solid obstacles randomly but uniformly distributed in the whole domain several relationships relating the computational time domain size and porosity are proposed additionally an expression that relates the hydraulic tortuosity to the porosity is proposed

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