Numerical schemes for the coupling of compressible and incompressible fluids in several space dimensions

TL;DR

This paper introduces efficient numerical schemes for simulating two-phase flows involving one compressible and one incompressible fluid, emphasizing coupling strategies that reduce computational costs while maintaining accuracy.

Contribution

It proposes new coupling strategies for compressible and incompressible Euler equations, including approximate methods, and compares their performance to fully compressible schemes.

Findings

Schemes show good agreement with standard algorithms

Reduced computational effort with approximate coupling strategies

Effective simulation of inviscid liquid-vapour flows

Abstract

We present a numerical scheme for immiscible two-phase flows with one compressible and one incompressible phase. Special emphasis lies in the discussion of the coupling strategy for compressible and incompressible Euler equations to simulate inviscid liquid-vapour flows. To reduce the computational effort further, we also introduce two approximate coupling strategies. The resulting schemes are compared numerically to a fully compressible scheme and show good agreement with these standard algorithm at lower numerical costs.