A compressible multifluid system with new physical relaxation terms

Didier Bresch (1) , Matthieu Hillairet (2)

1 LAMA - Laboratoire de Mathématiques
2 IMAG - Institut Montpelliérain Alexander Grothendieck

In this paper, we rigorously derive a new compressible multifluid system from compressible Navier-Stokes equations with density-dependent viscosity in the one-dimensional in space setting. More precisely, we propose and mathematically derive a generalization of the usual one velocity Baer-Nunziato model with a new relaxation term in the PDE governing the volume fractions. This new relaxation term encodes the change of viscosity and pressure between the different fluids. For the reader's convenience, we first establish a formal derivation in the bifluid setting using a WKB decomposition and then we rigorously justify the multifluid homogenized system using a kinetic formulation via Young measures characterization.

Mots clés: Baer-Nunziato; Compressible Navier–Stokes; Homogenization; Density-dependent viscosity; Effective flux; Multifluid systems; Young measures

Domaines: Equations aux dérivées partielles [math.AP]; Mécanique des fluides [physics.class-ph]

Didier Bresch, Matthieu Hillairet. A compressible multifluid system with new physical relaxation terms. Annales Scientifiques de l'École Normale Supérieure, 2019, 52 (2), pp.255-295. ⟨10.24033/asens.2387⟩. ⟨hal-01262617⟩