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

a new differential lattice boltzmann equation and its application to simulate incompressible flows on non uniform grids a new differential lattice boltzmann equation lbe is presented in this work which is derived from the standard lbe by using taylor series expansion only in spatial direction with truncation to the second order derivatives the obtained differential equation is not a wave like equation when a uniform grid is used the new differential lbe can be exactly reduced to the standard lbe the new differential lbe can be applied to solve irregular problems with the help of coordinate transformation the present scheme inherits the merits of the standard lbe the 2 d driven cavity flow is chosen as a test case to validate the present method favorable results are obtained and indicate that the present scheme has good prospects in practical applications

finite difference lattice boltzmann method for compressible thermal fluids a splitting method to solve the modeled lattice boltzmann equation the splitting technique permits the boundary conditions for the lattice boltzmann equation to be set as conveniently as those required for the finite difference solution of the navier stokes equations it is shown that the compressible navier stokes equation can be recovered fully from this approach however the formulation requires the solution of a poisson equation governing a secondorder tensor thus constructed the method has no arbitrary constants the proposed method is used to simulate thermalcouette flow aeroacoustics andshockstructureswithanextendedthermodynamicsmodel thesimulations are carried out using a high order finite difference scheme with a two dimensional nine velocity lattice all simulations are performed using a single relaxation time and a set of constants deduced from the derivation it is found that the finite difference lattice boltzmann method is able to correctly replicate viscous effects in thermal couette flows aeroacoustics andshockstructures thesolutionsobtainedareidenticaleithertoanalyticalresults or obtained by solving the compressible navier stokes equations using a direct numerical simulation technique

discretizations for the incompressible navier stokes equations based on the lattice boltzmann method a discrete velocity model with spatial and velocity discretization based on a lattice boltzmann method is considered in the low mach number limit a uniform numerical scheme for this model is investigated in the limit the scheme reduces to a finite difference scheme for the incompressible navier stokes equation which is a projection method with a second order spatial discretization on a regular grid the discretization is analyzed and the method is compared to chorin s original spatial discretization numerical results supporting the analytical statements are presented

acceleration of steady state lattice boltzmann simulations on non uniform mesh using local time step method in this paper the local time step method is applied to the lattice boltzmann method lbm on non uniform grid generalized form of interpolation supplemented lbm gilbm for steady flow simulations the local time step method is known to be an effective technique to accelerate the solution to the converged steady state on non uniform grid first code validation for global time step method is performed by solving flow around a cylinder at low reynolds numbers our results show good agreement with previous studies two dimensional flow simulations around an airfoil were performed in order to validate the code using the local time step method and the results are compared with the global time step solutions the pressure distribution and the aerodynamic coefficients of global and local time step results are in good agreement they are also consistent with the previous studies at the same time cpu time required to obtain the steady state solutions using the local time step are reduced by 70 80 compared with that using global time step

the unified structure of unbiased minimum variance reduced order filters a unified two stage functional filter utsff is proposed serving as a unified structure of unbiased minimum variance reduced order filters for linear time varying discrete time systems the utsff includes two parts one is for the main functional estimate which defines the main computing structure of the filter and the other is for the complementary functional estimate which is added to the former in order to further enhance the filtering performance the relationships between the utsff and existing reduced order filters are explored through the utsff a general procedure for applying a suitable unbiased minimum variance reduced order filter is given simulation examples are also given to illustrate the proposed results

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

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

lattice boltzmann accuracy in pore scale flow simulation we investigate the possibility of using nominally second order accurate techniques for resolving flow about solid boundaries as a means of improving accuracy and reducing grid resolution requirements in pore scale simulations an lbgk method is used to calculate flow in several geometries of increasing complexity using a first order accurate and two nominally second order accurate methods for no slip boundaries the geometries include uniform flow past an isolated sphere quadratic flow past a sphere near a wall flow through a bcc array of spheres and through a randomly packed bed of spheres the packed bed flows are also used to compare hydrodynamic dispersion results the results confirm second order accurate behavior where navier stokes flows are clearly developed however 3d pore scale simulations involve a trade off between resolution of the flow and the number of pore spaces and there is a resolution threshold below which certain flow features such as recirculation are not resolved we conjecture that most simulations will tend to operate near this threshold because of the competing demands for resolution and statistical accuracy we consider local flow features and the velocity distribution in addition to hydraulic permeability and drag to provide a fuller understanding of accuracy near this threshold

flow simulation around cambered airfoil by using conformal mapping and intermediate domain in lattice boltzmann method in this paper the developed interpolation lattice boltzmann method is used for simulation of unsteady fluid flow it combines the desirable features of the lattice boltzmann and the joukowski transformation methods this approach has capability to simulate flow around curved boundary geometries such as airfoils in a body fitted grid system simulation of unsteady flow around a cambered airfoil in a non uniform grid for the first time is considered to show the capability of this method for modeling of fluid flow around complex geometries and complicated long term periodic flow phenomena the developed solver is also coupled with a fast adaptive grid generator in addition the new approach retains all the advantages of the standard lattice boltzmann method the strouhal number the pressure the drag and the lift coefficients obtained from the simulations agree well with classical computational fluid dynamics simulations numerical studies for various test cases illustrate the strength of this new approach

accuracy of higher order lattice boltzmann methods for microscale flows with finite knudsen numbers accuracy of the lattice boltzmann lb method for microscale flows with finite knudsen numbers is investigated we employ up to the eleventh order gauss hermite quadrature for the lattice velocities and diffuse scattering boundary condition for fluid wall interactions detailed comparisons with the direct simulation monte carlo dsmc method and the linearized boltzmann equation are made for planar couette and poiseuille flows all higher order lb methods considered here give improved results as compared with the standard lb method the accuracy of the lb hierarchy however does not monotonically increase with the order of the gauss hermite quadrature at moderate and large knudsen numbers the results also show the sensitivity to a quadrature chosen even when the gauss hermite quadratures have the same order of formal accuracy among the schemes investigated here d2q16 is the most efficient method and offers a quantitative prediction in the slip and transition regimes the higher order lb methods predict the knudsen layer up to kn o 0 1 the knudsen layer however rapidly disappears when the knudsen number approaches unity due to a finite number of the lattice velocities while it is still present for kn o 1 in the boltzmann equation it is also found that the higher order lb methods adopted here do not capture the asymptotic behavior of the boltzmann equation at large knudsen numbers

a unified approach to whiteman s and ding helleseth s generalized cyclotomy over residue class rings the theory of cyclotomy dates back to gauss and has a number of applications in combinatorics coding theory and cryptography cyclotomy over a residue class ring bbzv can be divided into classical cyclotomy or generalized cyclotomy depending on v prime or composite in this paper we introduce a generalized cyclotomy of order d over bbzp1e1p2e2 pnen which includes whiteman s and ding helleseth s generalized cyclotomy as special cases here p1 p2 pn are pairwise distinct odd primes satisfying d pi 1 for all 1 i n and e1 e2 en are positive integers we derive some basic properties of the corresponding cyclotomic numbers and obtain a general formula to compute them via classical cyclotomic numbers as applications we completely solve an open problem and a conjecture on whiteman s generalized cyclotomy of order four over bbzp1p2 besides we also construct an infinite series of near optimal codebooks over bbzp1p2 as well as some infinite series of asymptotically optimal difference systems of sets over bbzp1e1p2e2 pnen

a multigrid solver for the discrete boltzmann equation this paper introduces a nonlinear multigrid solution approach for the discrete boltzmann equation discretized by an implicit second order finite difference scheme for simplicity we restrict the discussion to the stationary case a numerical example shows the drastically improved efficiency in comparison to the widely used lattice bathnagar gross krook lbgk approach

finite difference lattice boltzmann model for nonlinear convection diffusion equations in this paper a finite difference lattice boltzmann lb model for nonlinear isotropic and anisotropic convection diffusion equations is proposed in this model the equilibrium distribution function is delicately designed in order to recover the convection diffusion equation exactly different from the standard lb model the temporal and spatial steps in this model are decoupled such that it is convenient to study convection diffusion problem with the non uniform grid in addition it also preserves the advantage of standard lb model that the complex valued convection diffusion equation can be solved directly the von neumann stability analysis is conducted to discuss the stability region which can be used to determine the free parameters appeared in the model to test the performance of the model a series of numerical simulations of some classical problems including the diffusion equation the nonlinear heat conduction equation the sine gordon equation the gaussian hill problem the burgersfisher equation and the nonlinear schrdinger equation have also been carried out the results show that the present model has a second order convergence rate in space and generally it is also more accurate than the standard lb model

high order upwind compact finite difference lattice boltzmann method for viscous incompressible flows abstract in this work a high order upwind compact finite difference lattice boltzmann method ucdlbm is developed to efficiently solve viscous incompressible flow problems a fifth order upwind compact difference scheme is adopted to discretize the spatial derivatives of the lattice boltzmann equation and the third order total variation diminishing runge kutta scheme is utilized for the discretization of the temporal term compared to the existing central compact finite difference lattice boltzmann method cfdlbm the present ucdlbm can prevent non physical oscillations without filtering due to the natural dissipative property of upwind schemes three benchmark problems involving the taylor green vortex problem the doubly periodic shear layer flow problem and the lid driven square cavity flow problem are numerically solved to demonstrate the accuracy and efficiency of the present method numerical results computed are in good agreement with the analytical solution or other available numerical results and the present ucdlbm is less time consuming than the cfdlbm without degenerating the order of accuracy of the numerical solutions

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

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

several classes of binary sequences with three level autocorrelation in this correspondence we describe several classes of binary sequences with three level autocorrelation those classes of binary sequences are based on cyclic almost difference sets some classes of binary sequences have optimum autocorrelation

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

a fully implicit method for lattice boltzmann equations existing approaches for solving the lattice boltzmann equations with finite difference methods are explicit and semi implicit both have certain stability constraints on the time step size in this work a fully implicit second order finite difference scheme is developed we focus on a parallel highly scalable newton krylov ras algorithm for the solution of a large sparse nonlinear system of equations arising at each time step here ras is a restricted additive schwarz preconditioner based on a first order spatial discretization we show numerically that by using the fully implicit method the time step size is no longer constrained by the cfl condition and the newton krylov ras algorithm is scalable on a supercomputer with more than ten thousand processors moreover to calculate the steady state solution we investigate an adaptive time stepping strategy the total compute time required by the implicit method with adaptive time stepping is much smaller than that of an explicit method for several t

the linear complexity of whiteman s generalized cyclotomic sequences of period p m 1 q n 1 in this paper we mainly get three results first let p q be distinct primes with p 1 p q 1 q p 1 q 1 e we give a method to compute the linear complexity of whiteman s generalized cyclotomic sequences of period pm 1qn 1 second if e 4 we compute the exact linear complexity of whiteman s generalized cyclotomic sequences third if p q 5 mod 8 gcd p 1 q 1 4 and we fix a common primitive root g of both p and q then 2 h0 g which is a subgroup of the multiplicative group z pq if and only if whiteman s generalized cyclotomic numbers of order 4 depend on the decomposition pq a2 4b2 with 4 b

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

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

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

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

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

a solution adaptive lattice boltzmann method for two dimensional incompressible viscous flows a stencil adaptive lattice boltzmann method lbm is developed in this paper it incorporates the stencil adaptive algorithm developed by ding and shu 26 for the solution of navier stokes n s equations into the lbm calculation based on the uniform mesh the stencil adaptive algorithm refines the mesh by two types of 5 points symmetric stencils which are used in an alternating sequence for increased refinement levels the two types of symmetric stencils can be easily combined to form a 9 points symmetric structure using the one dimensional second order interpolation recently developed by wu and shu 27 along the straight line and the d2q9 model the adaptive lbm calculation can be effectively carried out note that the interpolation coefficients are only related to the lattice velocity and stencil size hence the simplicity of lbm is not broken down and the accuracy is maintained due to the use of adaptive technique much less mesh points are required in the simulation as compared to the standard lbm as a consequence the computational efficiency is greatly enhanced the numerical simulation of two dimensional lid driven cavity flows is carried out accurate results and improved efficiency are reached in addition the steady and unsteady flows over a circular cylinder are simulated to demonstrate the capability of proposed method for handling problems with curved boundaries the obtained results compare well with data in the literature

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

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

a hybrid wavelet based adaptive immersed boundary finite difference lattice boltzmann method for two dimensional fluid structure interaction abstract a second generation wavelet based adaptive finite difference lattice boltzmann method fd lbm is developed in this paper in this approach the adaptive wavelet collocation method awcm is firstly to the best of our knowledge incorporated into the fd lbm according to the grid refinement criterion based on the wavelet amplitudes of density distribution functions an adaptive sparse grid is generated by the omission and addition of collocation points on the sparse grid the finite differences are used to approximate the derivatives to eliminate the special treatments in using the fd based derivative approximation near boundaries the immersed boundary method ibm is also introduced into fd lbm by using the adaptive technique the adaptive code requires much less grid points as compared to the uniform mesh code as a consequence the computational efficiency can be improved to justify the proposed method a series of test cases including fixed boundary cases and moving boundary cases are invested a good agreement between the present results and the data in previous literatures is obtained which demonstrates the accuracy and effectiveness of the present awcm ib lbm

lattice boltzmann method on quadtree grids for simulating fluid flow through porous media a new automatic algorithm abstract during the past two decades the lattice boltzmann lb method has been introduced as a class of computational fluid dynamic methods for fluid flow simulations in this method instead of solving the navier stocks equation the boltzmann equation is solved to simulate the flow of a fluid this method was originally developed based on uniform grids however in order to model complex geometries such as porous media it can be very slow in comparison with other techniques such as finite differences and finite elements to eliminate this limitation a number of studies have aimed to formulate the lattice boltzmann on the unstructured grids this paper deals with simulating fluid flow through a synthetic porous medium using the lb method and on the quadtree grid structure to this end the lb method was used on nonuniform grids coupled with a technique for image reconstruction which resulted in the quadtree grids for simulation of fluid flow through porous media accuracy and efficiency of this algorithm is compared against the conventional lb method based on uniform grids while the decrease in computational time in the proposed lb method on nonuniform grids is found to be significant regarding the size of the initial and reconstructed images the same level of accuracy is obtained when compared with the conventional lb method on uniform grids

a mass conserving boundary condition for the lattice boltzmann equation method in lattice boltzmann lb simulations the widely used wall boundary conditions bcs proposed by filipova and hanel fh and mei luo and shyy mls result in constant mass leakage in certain circumstances in this paper we have analyzed the source of the leakage based on this analysis we propose a second order accurate mass conserving wall bc in our bc the distribution function at a wall node is decomposed into its equilibrium and non equilibrium parts the mass conservation is guaranteed by enforcing a mass conserving rule in the construction of the fictitious equilibrium distribution part we have shown through several benchmark test problems involving steady and unsteady flows that our new bc not only eliminates the constant mass leakage but also has many other advantages over the fh and mls bcs

autocorrelation values of generalized cyclotomic sequences of order two the generalized cyclotomic sequence of order two has several good randomness properties and behaves like the legendre sequence in several aspects we calculate the autocorrelation values of the generalized cyclotomic sequence of order two our result shows that this sequence could have very good autocorrelation property and pattern distributions of length two if the two primes are chosen properly

an immersed boundary method for fluids using the xfem and the hydrodynamic boltzmann transport equation abstract this paper presents a stabilized finite element formulation of the hydrodynamic boltzmann transport equation hbte to predict nearly incompressible fluid flow the hbte is discretized with hermite polynomials in the velocity variable and a streamline upwind petrov galerkin formulation is used to discretize the spatial variable a nonlinear stabilization scheme is presented from which a simple linear stabilization scheme is constructed in contrast to the navier stokes ns equations the hbte is a first order equation and allows for conveniently enforcing dirichlet conditions along immersed boundaries a simple and efficient formulation for enforcing dirichlet boundary conditions is presented and its accuracy is studied for immersed boundaries captured by the extended finite element method xfem numerical experiments indicate that both the linear and non linear stabilization methods are sufficiently accurate and stable but the linear formulation reduces the computational cost significantly the accuracy of enforcing boundary conditions is satisfactory and shows second order convergence as the mesh is refined augmenting the boundary condition formulation with a penalty term increases the accuracy of enforcing the boundary condition constraints but may degrade the accuracy of the global solution comparisons with results of a single relaxation time lattice boltzmann method show that the proposed finite element method features greater robustness and lesser dependence of the computational costs on the level of mesh refinement

optimal minimal order least squares estimators via the general two stage kalman filter a direct derivation of the optimal minimal order least squares estimator is presented using the general two stage kalman filter using this new result the reduced order estimators of o reilly 1982 and fairman and luk 1985 are readily shown to be equivalent a practical implementation issue to consider these two estimators is also addressed

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

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

lattice bgk model for incompressible navier stokes equation abstract most of the existing lattice boltzmann bgk models lbgk can be viewed as compressible schemes to simulate incompressible fluid flows the compressible effect might lead to some undesirable errors in numerical simulations in this paper a lbgk model without compressible effect is designed for simulating incompressible flows the incompressible navier stokes equations are exactly recovered from this incompressible lbgk model numerical simulations of the plane poiseuille flow the unsteady 2 d shear decaying flow the driven cavity flow and the flow around a circular cylinder are performed the results agree well with the analytic solutions and the results of previous studies

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

optimal filtering for systems with unknown inputs via the descriptor kalman filtering method this paper addresses globally optimal unbiased minimum variance state estimation for systems with unknown inputs that affect both the system and the output with the descriptor kalman filtering method it is shown that directly applying the conventional descriptor kalman filter dkf to the considered problem may not yield the globally optimal solution because the unknown input vector may not be estimable to remedy this problem three approaches are proposed to facilitate optimal filter design the transformed approach uses some input and output transformations the untrammeled approach does not require any transformations and the augmented approach reconstructs the unknown input dynamics then three 5 block forms of the extended dkf 5 block edkf are derived as globally optimal state estimators in the sense that the first two filters are equivalent to the recently developed extended recursive three step filter and the third is equivalent to the conventional augmented state kalman filter the relationship between the proposed edkfs and the existing results in the literature is addressed simulation results are given to illustrate the usefulness of the proposed filters

finite volume versus streaming based lattice boltzmann algorithm for fluid dynamics simulations a one to one accuracy and performance study a finite volume fv discretization method for the lattice boltzmann lb equation which combines high accuracy with limited computational cost is presented in order to assess the performance of the fv method we carry out a systematic comparison focused on accuracy and computational performances with the standard streaming lattice boltzmann equation algorithm in particular we aim at clarifying whether and in which conditions the proposed algorithm and more generally any fv algorithm can be taken as the method of choice in fluid dynamics lb simulations for this reason the comparative analysis is further extended to the case of realistic flows in particular thermally driven flows in turbulent conditions we report the successful simulation of high rayleigh number convective flow performed by a lattice boltzmann fv based algorithm with wall grid refinement

a finite difference lattice boltzmann method with second order accuracy of time and space for incompressible flow abstract in this paper a kind of finite difference lattice boltzmann method with the second order accuracy of time and space t2s2 fdlbm is proposed in this method a two stage time accurate discretization approach is applied to construct time marching scheme and the spatial gradient operator is discretized by a mixed difference scheme to maintain a second order accuracy in space it is shown that the previous finite difference lattice boltzmann method fdlbm guo and zhao 2003 is a special case of the t2s2 fdlbm through the von neumann analysis the stability of the method is analyzed and two specific t2s2 fdlbms are discussed the two t2s2 fdlbms are applied to simulate some incompressible flows with the non uniform grids compared with other high order fdlbms this two t2s2 fdlbms keep the simplicity of standard lattice boltzmann method compared with the previous fdlbm and lattice boltzmann method the two t2s2 fdlbms are more accurate and more stable the value of the courant friedrichs lewy condition number in our method can be up to 0 9 which also significantly improves the computational efficiency

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

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

simulation of flows around an impulsively started circular cylinder by taylor series expansion and least squares based lattice boltzmann method the two dimensional incompressible viscous flow past an impulsively started circular cylinder for a wide range of reynolds numbers re 20 9500 is studied computationally by using an explicit taylor series expansion and least squares based lattice boltzmann method the final equation for distribution function in our method is in an explicit form and essentially has no limitation on choice of mesh structure and lattice model it can be easily applied to simulation of flows with curved boundaries such as the problem considered in this work for the flow past an impulsively started circular cylinder numerical results obtained by present method agree very well with experimental data and computational results of navier stokes equations available in the literature

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

modeled boltzmann equation and its application to direct aeroacoustics simulation the bhatnagar gross and krook modeled boltzmann equation has been applied to simulate different fluid dynamics problems with varying degrees of success however its application to direct aeroacoustic computation is less successful one possible reason could be its inability to recover the state equation correctly for a diatomic gas and hence an inaccurate determination of the speed of sound the present study reports on the development of an improved modeled boltzmann equation for aeroacoustics simulation the approach is to modify the maxwellian distribution normally assumed for the equilibrium particle distribution function constraints imposed are the exact recovery of the state equation for a diatomic gas and the euler equations without invoking the small mach number assumption thus formulated a distribution function consisting of the maxwellian distribution plus three other terms that attempt to account for particle particle collisions is obtained a velocity lattice method is used to solve the improved modeled boltzmann equation using an equivalent lattice equilibrium distribution function the simulations are validated against benchmark aeroacoustic problems whose solutions are deduced from a direct numerical simulation of the euler equations the results of the improved modeled boltzmann equation obtained using a smaller computational domain are in excellent agreement with those deduced from direct numerical simulation using a larger computational domain thus verifying the viability and correctness of the modified equilibrium distribution function

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

generalized cyclotomic codes of length p sub 1 sup e 1 p sub t sup e t we first introduce a generalized cyclotomy of order 2 with respect to p sub 1 sup e 1 p sub t sup e t we then present two classes of new error correcting binary cyclic codes of length p sub 1 sup e 1 p sub t sup e t based on this generalized cyclotomy we prove either a square root bound or a similar bound on the minimum odd weight of those codes with length n p sub 1 sup e 1 p sub 2 sup e 2

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

investigation of stability and hydrodynamics of different lattice boltzmann models stability and hydrodynamic behaviors of different lattice boltzmann models including the lattice boltzmann equation lbe the differential lattice boltzmann equation dlbe the interpolation supplemented lattice boltzmann method islbm and the taylor series expansion and least square based lattice boltzmann method tllbm are studied in detail our work is based on the von neumann linearized stability analysis under a uniform flow condition the local stability and hydrodynamic dissipation behaviors are studied by solving the evolution operator of the linearized lattice boltzmann equations numerically our investigation shows that the lbe schemes with interpolations such as dlbe islbm and tllbm improve the numerical stability by increasing hyper viscosities at large wave numbers small scales it was found that these interpolated lbe schemes with the upwind interpolations are more stable than those with central interpolations because of much larger hyper viscosities

public key cryptosystems based on cubic finite field extensions the cryptographic properties of third order linear feedback shift register lfsr sequences over gf p are investigated a fast computational algorithm for evaluating the kth term of a characteristic sequence of order 3 is presented based on these properties a new public key distribution scheme and an rsa type encryption algorithm are proposed their security implementation information rate and computational cost for the new schemes are discussed

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

on reducing the order of kalman filters for discrete time stochastic systems having singular measurement noise a reduced order least squares state estimator is developed for estimating the states of a linear discrete time stochastic system having some outputs which are noise free

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

direct and large eddy simulation of turbulent flows on composite multi resolution grids by the lattice boltzmann method in order to properly address the simulation of complex weakly compressible turbulent flows the lattice boltzmann method originally designed for uniform structured grids needs to be extended to composite multi domain grids displaying various levels of spatial resolution therefore physical conditions must be specified to determine the mapping of statistical information about the populations of moving particles at the interface between two domains of different resolutions quite simply in terms of the probability distributions of the underlying discrete velocity boltzmann equation namely the continuity of the mass density and fluid momentum is fulfilled by imposing the continuity of the equilibrium part of these distributions whereas the discontinuity of the rate of strain tensor is ensured by applying a spatial transformation to the collision term of the discrete velocity boltzmann equation the latter condition allows us to explicitly account for the subgrid scale modeling in the treatment of resolution changes test computations of a turbulent plane channel flow have been carried out the lattice boltzmann scheme relies on the standard d3q19 lattice in a cell vertex representation and uses the bgk approximation for the collision term a shear improved variant of the smagorinsky viscosity is used to account for possible subgrid scale dynamics in a quasi direct numerical simulation at re t 180 with two levels of grid resolution the results are found in excellent agreement with reference data obtained by a high resolution pseudo spectral simulation in a large eddy simulation les at re t 395 with three levels of grid resolution the results compare reasonably well with high resolution reference data the accuracy is improved in comparison with a standard finite volume les performed with the same subgrid scale viscosity and comparable grid resolution by combining the simplicity and physical relevance of the shear improved smagorinsky model and the computational efficiency of the lattice boltzmann scheme here extended to composite multi resolution grids we believe that our proposal offers a high potential for the simulation of complex turbulent flows

three time integration methods for incompressible flows with discontinuous galerkin boltzmann method abstract this paper presents three time integration methods for incompressible flows with finite element method in solving the lattice bgk boltzmann equation the space discretization is performed using nodal discontinuous galerkin method which employs unstructured meshes with triangular elements and high order approximation degrees the time discretization is performed using three different kinds of time integration methods namely direct decoupling and splitting from the storage cost temporal accuracy numerical stability and time consumption we systematically compare three time integration methods then benchmark fluid flow simulations are performed to highlight efficient time integration methods numerical results are in good agreement with others or exact solutions

on the optimal unbiased functional filtering presents a simple solution to the optimal unbiased reduced order or functional filtering problem for linear time varying systems necessary and sufficient conditions for the existence of the obtained filter are given stability and convergence conditions are developed for the time invariant systems both continuous and discrete time cases are considered

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

viscosity of finite difference lattice boltzmann models two dimensional finite difference lattice boltzmann models for single component fluids are discussed and the corresponding macroscopic equations for mass and momentum conservation are derived by performing a chapman enskog expansion in order to recover the correct mass equation characteristic based finite difference schemes should be associated with the forward euler scheme for the time derivative while the space centered and second order upwind schemes should be associated to second order schemes for the time derivative in the incompressible limit the characteristic based schemes lead to spurious numerical contributions to the apparent value of the kinematic viscosity in addition to the physical value that enters the navier stokes equation formulae for these spurious numerical viscosities are in agreement with results of simulations for the decay of shear waves

stochastic finite difference lattice boltzmann method for steady incompressible viscous flows with the advent of state of the art computers and their rapid availability the time is ripe for the development of efficient uncertainty quantification uq methods to reduce the complexity of numerical models used to simulate complicated systems with incomplete knowledge and data the spectral stochastic finite element method ssfem which is one of the widely used uq methods regards uncertainty as generating a new dimension and the solution as dependent on this dimension a convergent expansion along the new dimension is then sought in terms of the polynomial chaos system and the coefficients in this representation are determined through a galerkin approach this approach provides an accurate representation even when only a small number of terms are used in the spectral expansion consequently saving in computational resource can be realized compared to the monte carlo mc scheme recent development of a finite difference lattice boltzmann method fdlbm that provides a convenient algorithm for setting the boundary condition allows the flow of newtonian and non newtonian fluids with and without external body forces to be simulated with ease also the inherent compressibility effect in the conventional lattice boltzmann method which might produce significant errors in some incompressible flow simulations is eliminated as such the fdlbm together with an efficient uq method can be used to treat incompressible flows with built in uncertainty such as blood flow in stenosed arteries the objective of this paper is to develop a stochastic numerical solver for steady incompressible viscous flows by combining the fdlbm with a ssfem validation against mc solutions of channel couette driven cavity and sudden expansion flows are carried out

brief paper on the global optimality of unbiased minimum variance state estimation for systems with unknown inputs in this paper a globally optimal filtering framework is developed for unbiased minimum variance state estimation for systems with unknown inputs that affect both the system state and the output the resulting optimal filters are globally optimal within the unbiased minimum variance filtering over all linear unbiased estimators globally optimal state estimators with or without output and or input transformations are derived through the global optimality evaluation of this research the performance degradation of the filter proposed by darouach zasadzinski and boutayeb darouach m zasadzinski m boutayeb m 2003 extension of minimum variance estimation for systems with unknown inputs automatica 39 867 876 is clearly illustrated and the global optimality of the filter proposed by gillijns and de moor gillijns s de moor b 2007b unbiased minimum variance input and state estimation for linear discrete time systems with direct feedthrough automatica 43 934 937 is further verified the relationship with the existing literature results is addressed a unified approach to design a specific globally optimal state estimator that is based on the desired form of the distribution matrix from the unknown input to the output is also presented a simulation example is given to illustrate the proposed results

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