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, multi-phase equations, elastoplastic equations, and resistive MHD equations. Combinations of systems of equations are usually solved by coupling fnite element for solid modelling and CFD models for fuid modelling or including material efects 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 fnite volume numerical schemes. We use a combination of sharp- and difuse-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-material 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 efect of the metal container material and its conductivity on the ignition of the combustible gas, as well as the efects of an additional dielectric coating, the sensitivity of the gas, and diferences between scenarios with sealed and pre-damaged metal surfaces.

Key words: Plasma modelling, Four states of matter, Lightning, Ignition, Combustible gas, Elastoplastic solids