A compressible multifluid system with new physical relaxation terms

TL;DR

This paper derives a new compressible multifluid system with novel relaxation terms from Navier-Stokes equations, capturing viscosity and pressure changes between fluids, and rigorously justifies it using kinetic formulations.

Contribution

It introduces a generalized multifluid model with new relaxation terms and provides a rigorous mathematical derivation from fundamental fluid equations.

Findings

Derivation of a new multifluid system with relaxation terms

Mathematical justification using Young measures

Extension of classical models to include viscosity and pressure changes

Abstract

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.