Numerical passage from kinetic to fluid equations
SIAM Journal on Numerical Analysis
Simulation of cavity flow by the lattice Boltzmann method
Journal of Computational Physics
Stability analysis of lattice Boltzmann methods
Journal of Computational Physics
Higher order approximation methods for the Boltzmann equation
Journal of Computational Physics
A novel thermal model for the lattice Boltzmann method in incompressible limit
Journal of Computational Physics
Incompressible limits of lattice Boltzmann equations using multiple relaxation times
Journal of Computational Physics
Asymptotic analysis of the lattice Boltzmann equation
Journal of Computational Physics
Editorial: Mesoscopic methods in engineering and science
Computers & Mathematics with Applications
Lattice Boltzmann simulations of thermal convective flows in two dimensions
Computers & Mathematics with Applications
Lattice Boltzmann magnetohydrodynamics with current-dependent resistivity
Journal of Computational Physics
Computers & Mathematics with Applications
Lattice Boltzmann algorithms without cubic defects in Galilean invariance on standard lattices
Journal of Computational Physics
Hi-index | 0.10 |
The lattice Boltzmann space/time discretisation, as usually derived from integration along characteristics, is shown to correspond to a Strang splitting between decoupled streaming and collision steps. Strang splitting offers a second-order accurate approximation to evolution under the combination of two non-commuting operators, here identified with the streaming and collision terms in the discrete Boltzmann partial differential equation. Strang splitting achieves second-order accuracy through a symmetric decomposition in which one operator is applied twice for half timesteps, and the other operator is applied once for a full timestep. We show that a natural definition of a half timestep of collisions leads to the same change of variables that was previously introduced using different reasoning to obtain a second-order accurate and explicit scheme from an integration of the discrete Boltzmann equation along characteristics. This approach extends easily to include general matrix collision operators, and also body forces. Finally, we show that the validity of the lattice Boltzmann discretisation for grid-scale Reynolds numbers larger than unity depends crucially on the use of a Crank-Nicolson approximation to discretise the collision operator. Replacing this approximation with the readily available exact solution for collisions uncoupled from streaming leads to a scheme that becomes much too diffusive, due to the splitting error, unless the grid-scale Reynolds number remains well below unity.