Discretizations for the Incompressible Navier--Stokes Equations Based on the Lattice Boltzmann Method
- 1 January 2000
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Scientific Computing
- Vol. 22 (1) , 1-19
- https://doi.org/10.1137/s1064827599357188
Abstract
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.Keywords
This publication has 30 references indexed in Scilit:
- The lattice Boltzmann equation: theory and applicationsPublished by Elsevier ,2002
- A lattice Boltzmann model for Jeffreys viscoelastic fluidEurophysics Letters, 1998
- A priori derivation of the lattice Boltzmann equationPhysical Review E, 1997
- Uniformly Accurate Schemes for Hyperbolic Systems with RelaxationSIAM Journal on Numerical Analysis, 1997
- Derivation of the Lattice Boltzmann Method by Means of the Discrete Ordinate Method for the Boltzmann EquationJournal of Computational Physics, 1997
- Physical symmetry and lattice symmetry in the lattice Boltzmann methodPhysical Review E, 1997
- Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann methodPhysical Review A, 1992
- Fluid dynamic limits of kinetic equations. I. Formal derivationsJournal of Statistical Physics, 1991
- Incompressible navier‐stokes and euler limits of the boltzmann equationCommunications on Pure and Applied Mathematics, 1989
- Numerical solution of the Navier-Stokes equationsMathematics of Computation, 1968