On Riemann Solvers and Kinetic Relations for Isothermal Two-Phase Flows with Surface Tension

TL;DR

This paper develops new well-posed Riemann solvers for isothermal two-phase flows with surface tension, enabling accurate simulations of phase transitions and interface dynamics under complex conditions.

Contribution

It introduces novel well-posedness theorems and computable Riemann solvers that handle general equations of state, metastable data, and curvature effects in two-phase flow.

Findings

Validated Riemann solver against experimental data

Enabled reliable simulations of complex two-phase flow scenarios

Improved computational efficiency for interface tracking

Abstract

We consider a sharp-interface approach for the inviscid isothermal dynamics of compressible two-phase flow, that accounts for phase transition and surface tension effects. To fix the mass exchange and entropy dissipation rate across the interface kinetic relations are frequently used. The complete uni-directional dynamics can then be understood by solving generalized two-phase Riemann problems. We present new well-posedness theorems for the Riemann problem and corresponding computable Riemann solvers, that cover quite general equations of state, metastable input data and curvature effects. The new Riemann solver is used to validate different kinetic relations on physically relevant problems including a comparison with experimental data. Riemann solvers are building blocks for many numerical schemes that are used to track interfaces in two-phase flow. It is shown that the new Riemann solver enables reliable and efficient computations for physical situations that could not be treated before.