A Projection Method for Compressible Generic Two-Fluid Model

TL;DR

This paper introduces a novel projection method for viscous compressible two-fluid flows, extending existing techniques to ensure energy stability and accurate pressure determination in complex flow scenarios.

Contribution

The work develops a new projection method tailored for viscous compressible two-fluid models, ensuring stability and accurate pressure calculation, which was not addressed in prior methods.

Findings

Proves the energy stability of the numerical scheme.

Demonstrates the method's validity through three numerical tests.

Extends the projection method to viscous compressible two-fluid flows.

Abstract

A new projection method for a generic two-fluid model is presented in this work. Specifically, we extend the projection method, originally designed for single-phase variable density incompressible and compressible flows, to viscous compressible two-fluid flows. The key idea is that the single pressure $p$ can be uniquely determined by the products of volume fractions and densities $\phi_k \rho_k$, of the two fluids. Additionally, the stability of the method is ensured by appropriately assigning intermediate step variables at the time-discrete level and incorporating a stabilizing term at the fully discrete level. We prove the energy stability of the proposed numerical scheme, and its validity is demonstrated through three numerical tests.