arXiv subjects

Bennett Clayton

Publications and source records attributed to Bennett Clayton.

4 recordsLinked to original sources

arXiv2026

Analysis, thermodynamics, and a numerical 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 preserving methods for this model. A novel numerical method is presented for solving the highly nonlinear system for the equilibrated pressure and temperature with an arbitrary number of materials. This new method is compared with some traditional iterative solvers through a collection of different tests. 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.

math.NA↗

arXiv2025

Second-order invariant-domain preserving approximation to the multi-species Euler equations

This work is concerned with constructing a second-order, invariant-domain preserving approximation of the compressible multi-species Euler equations where each species is modeled by an ideal gas equation of state. We give the full solution to the Riemann problem and derive its maximum wave speed. The maximum wave speed is used in constructing a first-order invariant-domain preserving approximation. We then extend the methodology to second-order accuracy and detail a convex limiting technique which is used for preserving the invariant domain. Finally, the numerical method is verified with analytical solutions and then validated with several benchmarks and laboratory experiments.

math.NA↗

arXiv2025

Preserving the minimum principle on the entropy for the compressible Euler Equations with general equations of state

This paper is concerned with constructing an invariant-domain preserving approximation technique for the compressible Euler equations with general equations of state that preserves the minimum principle on the physical entropy. We derive a sufficient wave speed estimate for the Riemann problem under some mild thermodynamic assumptions on the equation of state. This minimum principle is guaranteed through the use of discrete auxiliary states which are in the invariant domain when using this new wave speed estimate. Finally, we numerically illustrate the proposed methodology.

math.NA↗

arXiv2022

Robust second-order approximation of the compressible Euler equations with an arbitrary equation of state

This paper is concerned with the approximation of the compressible Euler equations supplemented with an arbitrary or tabulated equation of state. The proposed approximation technique is robust, formally second-order accurate in space, invariant-domain preserving, and works for every equation of state, tabulated or analytic, provided the pressure is nonnegative. An entropy surrogate functional that grows across shocks is proposed. The numerical method is verified with novel analytical solutions and then validated with several computational benchmarks seen in the literature.

math.NA↗