An interface capturing method for liquid-gas flows at low-Mach number

TL;DR

This paper introduces a novel numerical method for simulating low-Mach number liquid-gas flows, combining a Volume of Fluid interface capturing technique with a low-Mach asymptotic expansion of Navier-Stokes equations, enabling efficient and accurate multiphase flow modeling.

Contribution

The paper presents a new Eulerian numerical approach that integrates a VOF interface method with a low-Mach expansion of Navier-Stokes equations, improving simulation accuracy for multiphase flows.

Findings

Validated with five benchmark test cases.

Achieved second-order accuracy in time and space.

Successfully captured large density variations and heat transfer.

Abstract

Multiphase, compressible and viscous flows are of crucial importance in a wide range of scientific and engineering problems. Despite the large effort paid in the last decades to develop accurate and efficient numerical techniques to address this kind of problems, current models need to be further improved to address realistic applications. In this context, we propose a numerical approach to the simulation of multiphase, viscous flows where a compressible and an incompressible phase interact in the low-Mach number regime. In this frame, acoustics is neglected but large density variations of the compressible phase can be accounted for as well as heat transfer, convection and diffusion processes. The problem is addressed in a fully Eulerian framework exploiting a low-Mach number asymptotic expansion of the Navier-Stokes equations. A Volume of Fluid approach (VOF) is used to capture the liquid-gas interface, built on top of a massive parallel solver, second order accurate both in time and space. The second-order-pressure term is treated implicitly and the resulting pressure equation is solved with the eigenexpansion method employing a robust and novel formulation. We provide a detailed and complete description of the theoretical approach together with information about the numerical technique and implementation details. Results of benchmarking tests are provided for five different test cases.