On the stability of a relative velocity lattice Boltzmann scheme for compressible Navier-Stokes equations

François Dubois (1, 2) , Tony Fevrier (2) , Benjamin Graille (2)

1 LMSSC - Laboratoire de Mécanique des Structures et des Systèmes Couplés
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

This paper studies the stability properties of a two dimensional relative velocity scheme for the Navier-Stokes equations. This scheme inspired by the cascaded scheme has the particularity to relax in a frame moving with a velocity field function of space and time. Its stability is studied first in a linear context then on the non linear test case of the Kelvin-Helmholtz instability. The link with the choice of the moments is put in evidence. The set of moments of the cascaded scheme improves the stability of the d’Humières scheme for small viscosities. On the contrary, a relative velocity scheme with the usual set of moments deteriorates the stability.

Domaines: Analyse numérique [math.NA]

François Dubois, Tony Fevrier, Benjamin Graille. On the stability of a relative velocity lattice Boltzmann scheme for compressible Navier-Stokes equations. 2015. ⟨hal-01113599⟩