Enhanced Diffuse Interface Method for Multiphase Flow Simulations Across All Mach Numbers
Ghanshyam Bharate, J. C. Mandal
TL;DR
This work addresses accurate all-Mach-number simulation of compressible multiphase flows using a six-equation diffuse-interface model with instantaneous relaxation. A Thornber-type low-Mach correction is integrated into an HLLC Riemann solver to reduce excessive numerical diffusion without imposing a global time-step restriction. Asymptotic analyses of both the continuous and semi-discrete systems demonstrate that the corrected scheme reproduces the correct pressure scaling in the low-Mach limit and aligns with the physical equilibrium behavior. The method is validated across diverse test cases, including subsonic nozzle flow, dam-break, low-amplitude sloshing, and shock–bubble interactions, showing improved symmetry, interface smoothness, and agreement with analytical and experimental benchmarks.
Abstract
This paper enhances the Diffuse Interface Method (DIM) for simulating compressible multiphase flows across all Mach numbers by addressing the accuracy challenges posed at low Mach regimes. A correction to the Riemann solver is introduced, designed to mitigate excessive numerical diffusion while maintaining simplicity and efficiency. The validity of this correction is established through rigorous asymptotic analysis of the governing equations and their discrete counterparts. The proposed correction is implemented within a six-equation model framework with instantaneous relaxation using an HLLC-type solver. Numerical test cases demonstrate significant improvements in accuracy, confirming the effectiveness of the approach in capturing multiphase flow dynamics across a wide range of Mach numbers.