# A multi-physics methodology for four-states of matter

## TL;DR

This paper introduces a unified numerical approach for simulating four different states of matter simultaneously, enabling complex multi-physics problems to be modeled on a single computational framework.

## Contribution

It develops a novel hyperbolic formulation and mixed-material Riemann solvers for coupled multi-physics systems, allowing full discretization of all matter states in one scheme.

## Key findings

- Successfully simulated ignition scenarios involving gas, liquid, solids, and plasma.
- Demonstrated the method's ability to handle complex material interfaces and boundary conditions.
- Provided insights into ignition processes influenced by material properties and configurations.

## Abstract

We propose a numerical methodology for the simultaneous numerical simulation of four states of matter; gas, liquid, elastoplastic solids and plasma. The distinct, interacting physical processes are described by a combination of compressible, inert and reactive forms of the Euler equations, multiphase equations, elastoplastic equations and resistive MHD equations. Combinations of systems of equations are usually solved by coupling finite element for solid modelling and CFD models for fluid modelling or including material effects through boundary conditions rather than full material discretisation. Our simultaneous solution methodology lies on the recasting of all the equations in the same, hyperbolic form allowing their solution on the same grid with the same finite-volume numerical schemes. We use a combination of sharp and diffuse interface methods to track or capture material interfaces, depending on the application. The communication between the distinct systems of equations (i.e., materials separated by sharp interfaces) is facilitated by means of mixed-material Riemann solvers at the boundaries of the systems, which represent physical material boundaries. To this end we derive approximate mixed Riemann solvers for each pair of the above models based on characteristic equations. To demonstrate the applicability of the new methodology we consider a case study where we investigate the possibility of ignition of a combustible gas that lies over a liquid in a metal container that is struck by a plasma-arc akin to a lightning strike. We study the effect on the ignition of the metal container material and conductivity, of the presence of a dielectric coating, of insensitive combustible gases and sealed and pre-damaged metal surfaces.