Highly Robust High-Order Numerical Framework for Solving Six-Equation Compressible Two-Phase Flow Model with Phase Change

Abstract The six-equation, single-velocity, two-phase flow model based on the diffuse-interface method (DIM) with stiff pressure relaxation has recently gained attention for its ability to handle metastable fluids, ensure robust positivity of volume fractions, and yield effective sound speeds consistent with Wood’s law. However, the presence of nonconservative terms in the phasic energy equations poses substantial challenges for numerical simulation, particularly in shock–interface interaction problems. In this work, we develop a general numerical framework for this model that achieves high fidelity, low dissipation, and strong robustness, while also accounting for phase change via additional source terms. First, we introduce a path-conservative Harten–Lax–van Leer–Contact (HLLC) solver grounded in Dal Maso–LeFloch–Murat (DLM) theory, enabling high-fidelity resolution of shock–interface interaction problems with phase change. This approach allows wave speeds to be captured more accurately, even in the presence of strong shock waves. Second, we propose a hybrid WENO–MOOD framework that combines high-resolution Weighted Essentially Non-Oscillatory (WENO) schemes with a posteriori Multidimensional Optimal Order Detection (MOOD), reducing numerical dissipation and enhancing robustness near dynamically generated interfaces. An improved MOOD technique, which limits phasic rather than mixture sound speed, enables the application of high-order WENO schemes to phase change problems. This approach allows for more accurate calculation of phase generation compared to traditional Monotone Upstream-centered Schemes for Conservation Laws (MUSCL), and significantly improves robustness when simulating phase change processes using high-order schemes. Third, by reformulating the mass transfer operator as a single nonlinear temperature equation, we further improve the relaxation method for phase change, enhancing robustness and reducing computational cost. A series of benchmark tests for compressible two-phase flows with phase transition demonstrate that WENO–MOOD delivers superior interface capturing and resolves more phase-change-induced flow structures than the conventional MUSCL scheme, while the improved relaxation method significantly reduces computational cost. This study provides a comprehensive assessment of numerical strategies for multiphase flow models and offers practical guidelines for the accurate and efficient simulation of phase-transition phenomena.