An all-mach HLLC based scheme for multi-phase flow with surface tension

This article presents an all-Mach method for two-phase inviscid flow in the presence of surface tension. A modified version of the Hartens, Lax, Leer and Contact (HLLC) approximate Riemann solver based on the work by Garrick et al., (2017) is developed and combined with the popular Volume of Fluid (VoF) method: Compressive Interface Capturing Scheme for Arbitrary Meshes (Ubbink & Issa, 1999) (CICSAM). This novel combination yields a scheme with both HLLC shock capturing as well as accurate liquid-gas interface tracking characteristics. The sonic and two-phase properties of the scheme are assessed using the popular advecting bubble, the Gas-Liquid Riemann problem, and the under-water explosion. The implementation of surface tension in the scheme is verified via the classic static bubble configuration, and the popular Rayleigh-Plesset collapse problem. For the static bubble, the spurious currents are of the order 10−8 demonstrating that the scheme is well-balanced. For the Rayleigh-Plesset problem, the maximum relative error on the minimum radius of collapse is found to be within 5% on the coarsest mesh.