2011/06/06 by Francis Filbet, Filbet, Francis
Engineering · Mathematics · #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Gas Dynamics and Kinetic Theory #Lattice Boltzmann Simulation Studies #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1106.1020
openalex publication_date 2011/06/06 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
In this paper we present a fully deterministic method for the numerical\nsolution to the Boltzmann equation of rarefied gas dynamics in a bounded domain\nfor multi-scale problems. Periodic, specular reflection and diffusive boundary\nconditions are discussed and investigated numerically. The collision operator\nis treated by a Fourier approximation of the collision integral, which\nguarantees spectral accuracy in velocity with a computational cost of\nN ,\log(N), where N is the number of degree of freedom in velocity space.\nThis algorithm is coupled with a second order finite volume scheme in space and\na time discretization allowing to deal for rarefied regimes as well as their\nhydrodynamic limit. Finally, several numerical tests illustrate the efficiency\nand accuracy of the method for unsteady flows (Poiseuille flows, ghost effects,\ntrend to equilibrium).\n