On steady-state preserving spectral methods for homogeneous Boltzmann equations

Francis Filbet (1, 2) , Lorenzo Pareschi (3) , Thomas Rey (4, 5)

1 MMCS - Modélisation mathématique, calcul scientifique
2 KALiFFE - Kinetic models AppLIed for Future of Fusion Energy
3 Department of Mathematics and Informatics
4 RAPSODI - Reliable numerical approximations of dissipative systems
5 CSCAMM - Center for Scientific Computation and Mathematical Modeling

In this note, we present a general way to construct spectral methods for the collision operator of the Boltzmann equation which preserves exactly the Maxwellian steady state of the system. We show that the resulting method is able to approximate with spectral accuracy the solution uniformly in time.

Domaines: Analyse numérique [math.NA]

Francis Filbet, Lorenzo Pareschi, Thomas Rey. On steady-state preserving spectral methods for homogeneous Boltzmann equations. Comptes Rendus. Mathématique, 2015, 353 (4), pp.309-314. ⟨10.1016/j.crma.2015.01.015⟩. ⟨hal-01053930⟩