  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.
