An All-Mach Number HLLC-Based Scheme for Multi-Phase Flow with Surface Tension

This paper presents an all-Mach method for two-phase inviscid flow in the presence of surface tension. A modified version of the Hartens-Lax-van Leer Contact (HLLC) solver is developed and combined for the first time with a widely used volume-of-fluid (VoF) method: the compressive interface capturing scheme for arbitrary meshes (CICSAM). This novel combination yields a scheme with both HLLC shock capturing as well as accurate liquid-gas interface tracking characteristics. It is achieved by reconstructing non-conservative (primitive) variables in a consistent manner to yield both robustness and accuracy. Liquid-gas interface curvature is computed via height functions and the convolution method. We emphasize the use of VoF in the interest of interface accuracy when modelling surface tension effects. The method is validated using a range of test-cases available in the literature. The results show flow features that are in sensible agreement with previous experimental and numerical work. In particular, the use of the HLLC-VoF combination leads to a sharp volume fraction and energy field with improved accuracy.

Automated summary

This paper introduces an all-Mach method for two-phase inviscid flow with surface tension effects, combining a modified HLLC solver with the CICSAM VoF method to achieve shock capturing and accurate interface tracking characteristics. Reconstruction of non-conservative variables is used for robustness and accuracy, with liquid-gas interface curvature computed through height functions and convolution. Validation using various test cases shows agreement with previous experimental and numerical work, particularly demonstrating improved accuracy in volume fraction and energy fields with the HLLC-VoF combination.