On lattice Boltzmann scheme, finite volumes and boundary conditions

Abstract

We develop the idea that a natural link between Boltzmann schemes and finite volumes exists naturally: the conserved mass and momentum during the collision phase of the Boltzmann scheme induces general expressions for mass and momentum fluxes. We treat a unidimensional case and focus our development in two dimensions on possible flux boundary conditions. Several test cases show that a high level of accuracy can be achieved with this scheme.

References in corpus (2)

• Equivalent partial differential equations of a lattice Boltzmann scheme
• Partial Riemann problem, boundary conditions, and gas dynamics

Cited by in corpus (4)

• Stable lattice Boltzmann schemes with a dual entropy approach for monodimensional nonlinear waves
• Multidimensional fully adaptive lattice Boltzmann methods with error control based on multiresolution analysis
• Chapman-Enskog Analysis of Finite Volume Lattice Boltzmann Schemes
• On triangular lattice Boltzmann schemes for scalar problems