Abstract

Multiphase phenomena are prevalent in natural environments, daily life, and industrial applications, playing a crucial role in materials development, energy chemical engineering, and geodynamic processes. In geological reservoirs, they significantly impact the safety, efficiency, and economics of energy recovery. Due to the complex and inaccessible nature of underground environments and cross-scale properties, these challenges necessitate mathematical modeling and numerical simulations. Phase equilibrium calculations and multiphase flow simulations are essential static and dynamic aspects of these phenomena, respectively. Thermodynamic consistency (energy minimization) is a key attribute of these physical models. Consequently, it is possible to design energy-stable numerical algorithms that adhere to these physical principles, ensuring the conservation of mass, momentum, and energy dissipation at the discrete level. Energy-stable schemes are proposed and validated in our work for (1) liquid-gas phase equilibrium calculations; (2) two-phase flow with large density contrast based on the diffuse interface and CCFD Eulerian mesh framework; and (3) two-phase flow based on the diffuse interface and smoothed particle hydrodynamics (SPH) mesh-free Lagrangian framework. These energy-stable schemes enhance numerical stability and the robustness of modeling methods