Averaged models for compressible two-phase stratified flows on thin domains

TL;DR

This paper derives simplified two-phase flow models for thin domains by asymptotic analysis of Navier-Stokes equations, allowing for two-velocity and one-pressure descriptions in compressible stratified flows.

Contribution

It introduces a novel asymptotic derivation method that recovers source terms and two-velocity models directly from the Navier-Stokes equations for thin domain two-phase flows.

Findings

Derived two-velocity one-pressure models in barotropic case

Extended models to full Navier-Stokes-Fourier case

Provided a systematic asymptotic analysis framework

Abstract

This paper deals with the derivation of compressible two-phase flow models. We use a thin domain approximation of a two-layer configuration governed by the Navier-Stokes equations, following the works [H. B. Stewart and B. Wendroff, J. Comp. Phys., 56 (1984)] and [V. H. Ransom and D. L. Hicks, J. Comput. Phys., 75 (1988)]. In order to recover source terms and two-velocity models directly from this asymptotic analysis, we remove the continuity of the tangential component of the velocity at the interface, and properly scale friction and viscosity coefficients. We are then able to derive two-velocity one-pressure models, first in the barotropic case and then in the full Navier-Stokes-Fourier case.