On the scope of the method of modified equations
SIAM Journal on Scientific and Statistical Computing
A critical analysis of the modified equation technique of Warming and Hyett
Journal of Computational Physics
A Knudsen layer theory for lattice gases
Proceedings of the NATO advanced research workshop on Lattice gas methods for PDE's : theory, applications and hardware: theory, applications and hardware
SIAM Journal on Numerical Analysis
Lattice Boltzmann method for 3-D flows with curved boundary
Journal of Computational Physics
Cellular Automata: A Discrete Universe
Cellular Automata: A Discrete Universe
Journal of Computational Physics
A lattice-Boltzmann relaxation scheme for coupled convection-radiation systems
Journal of Computational Physics
Asymptotic analysis of multiple-relaxation-time lattice Boltzmann schemes for mixture modeling
Computers & Mathematics with Applications
Boundary forces in lattice Boltzmann: Analysis of Momentum Exchange algorithm
Computers & Mathematics with Applications
Equivalent partial differential equations of a lattice Boltzmann scheme
Computers & Mathematics with Applications
Convergence of lattice Boltzmann methods for Stokes flows in periodic and bounded domains
Computers & Mathematics with Applications
A comparative study of the LBE and GKS methods for 2D near incompressible laminar flows
Journal of Computational Physics
Scale-Splitting Error in Complex Automata Models for Reaction-Diffusion Systems
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part II
Error Investigations in Complex Automata Models for Reaction-Diffusion Systems
ACRI '08 Proceedings of the 8th international conference on Cellular Automata for Reseach and Industry
TeraFLOP computing on a desktop PC with GPUs for 3D CFD
International Journal of Computational Fluid Dynamics - Mesoscopic Methods And Their Applications To CFD
Lattice Boltzmann modeling of microchannel flow in slip flow regime
Journal of Computational Physics
Journal of Computational Physics
Lattice Boltzmann simulations of 2D laminar flows past two tandem cylinders
Journal of Computational Physics
A lattice Boltzmann method for immiscible multiphase flow simulations using the level set method
Journal of Computational Physics
Asymptotic analysis of extrapolation boundary conditions for LBM
Computers & Mathematics with Applications
Adiabatic perturbations for compactons under dissipation and numerically-induced dissipation
Journal of Computational Physics
Asymptotic analysis of Complex Automata models for reaction--diffusion systems
Applied Numerical Mathematics
Optimal preconditioning of lattice Boltzmann methods
Journal of Computational Physics
Computers & Mathematics with Applications
Comparison of analysis techniques for the lattice Boltzmann method
Computers & Mathematics with Applications
Second order interpolation of the flow field in the lattice Boltzmann method
Computers & Mathematics with Applications
Analysis of open boundary effects in unsteady lattice Boltzmann simulations
Computers & Mathematics with Applications
Pressure boundary condition for the lattice Boltzmann method
Computers & Mathematics with Applications
Computers & Mathematics with Applications
A combined lattice BGK/level set method for immiscible two-phase flows
Computers & Mathematics with Applications
Journal of Computational Physics
Journal of Computational Physics
On a superconvergent lattice Boltzmann boundary scheme
Computers & Mathematics with Applications
On the stability structure for lattice Boltzmann schemes
Computers & Mathematics with Applications
Pressure condition for lattice Boltzmann methods on domains with curved boundaries
Computers & Mathematics with Applications
A lattice Boltzmann approach for free-surface-flow simulations on non-uniform block-structured grids
Computers & Mathematics with Applications
Journal of Computational Physics
Optimal low-dispersion low-dissipation LBM schemes for computational aeroacoustics
Journal of Computational Physics
Application of Lattice Boltzmann Method to sensitivity analysis via complex differentiation
Journal of Computational Physics
Journal of Computational Physics
Artificial compressibility method and lattice Boltzmann method: Similarities and differences
Computers & Mathematics with Applications
Multi-thread implementations of the lattice Boltzmann method on non-uniform grids for CPUs and GPUs
Computers & Mathematics with Applications
Link-wise artificial compressibility method
Journal of Computational Physics
An interpretation and derivation of the lattice Boltzmann method using Strang splitting
Computers & Mathematics with Applications
Stable lattice Boltzmann schemes with a dual entropy approach for monodimensional nonlinear waves
Computers & Mathematics with Applications
Lattice Boltzmann outflow treatments: Convective conditions and others
Computers & Mathematics with Applications
On enhanced non-linear free surface flow simulations with a hybrid LBM-VOF model
Computers & Mathematics with Applications
Lattice Boltzmann magnetohydrodynamics with current-dependent resistivity
Journal of Computational Physics
A lattice Boltzmann method for immiscible two-phase Stokes flow with a local collision operator
Computers & Mathematics with Applications
Lattice Boltzmann method for the convection-diffusion equation in curvilinear coordinate systems
Journal of Computational Physics
Computers & Mathematics with Applications
Hi-index | 31.53 |
In this article we analyze the lattice Boltzmann equation (LBE) by using the asymptotic expansion technique. We first relate the LBE to the finite discrete-velocity model (FDVM) of the Boltzmann equation with the diffusive scaling. The analysis of this model directly leads to the incompressible Navier-Stokes equations, as opposed to the compressible Navier-Stokes equations obtained by the Chapman-Enskog analysis with convective scaling. We also apply the asymptotic analysis directly to the fully discrete LBE, as opposed to the usual practice of analyzing a continuous equation obtained through the Taylor-expansion of the LBE. This leads to a consistency analysis which provides order-by-order information about the numerical solution of the LBE. The asymptotic technique enables us to analyze the structure of the leading order errors and the accuracy of numerically derived quantities, such as vorticity. It also justifies the use of Richardson's extrapolation method. As an example, a two-dimensional Taylor-vortex flow is used to validate our analysis. The numerical results agree very well with our analytic predictions.