Analysis, thermodynamics, and a numeric solver for a pressure-temperature equilibrium closure of the four-equation model

We analyze an often used closure model for multi-material hydrodynamics where pressure temperature equilibrium (PTE) is assumed for every state; emphasis is placed on tabular equations of state. This multi-material model is often referred to as the four-equation model. The identification of the admissible set is presented and is proven to be convex, setting the foundation for development of invariant-domain methods for this model. A novel, robust, and efficient method is presented for solving the highly nonlinear system for the equilibrated pressure and temperature with an arbitrary number of materials. Additionally, we provide a detailed analysis of the thermodynamics of the mixture model for general equations of state and prove existence and uniqueness of the pressure-temperature equilibrium solution under some thermodynamic assumptions.