A Path-Conservative Method for a Weakly Compressible Two-Phase Model with Surface Tension

TL;DR

This paper introduces a novel path-conservative numerical scheme for weakly compressible two-phase flows with surface tension, enabling accurate simulations without separate discretization of surface tension effects.

Contribution

A new HLLC-type path-conservative scheme for weakly compressible two-phase models that includes capillary effects directly in the formulation.

Findings

Effective handling of surface tension without separate discretization

High-order accuracy achieved with local solution reconstruction

Validated on benchmark two-phase flow problems

Abstract

When extended to two-phase flows, weakly compressible models lead to a non-conservative system, which precludes its treatment using standard finite volume techniques. In this paper, a novel HLLC-type path-conservative scheme is formulated for the weakly compressible two-phase model. Furthermore, capillary effects are included in the proposed path-conservative scheme, eliminating the need to discretize surface tension terms separately. The first-order path-conservative formulation is combined with a local solution reconstruction technique to obtain high-order spatial accuracy. The solver is tested on several benchmark two-phase flow problems to demonstrate its efficacy.