  This article presents a multi-physics methodology for the numerical
simulation of physical systems that involve the non-linear interaction of
multi-phase reactive fluids and elastoplastic solids, inducing high
strain-rates and high deformations. Each state of matter is governed by a
single system of non-linear, inhomogeneous partial differential equations,
which are solved simultaneously on the same computational grid, and do not
require special treatment of immersed boundaries. To this end, the governing
equations for solid and reactive multiphase fluid mechanics are written in the
same mathematical form and are discretised on a regular Cartesian mesh. All
phase and material boundaries are treated as diffuse interfaces. An
interface-steepening technique is employed at material boundaries to keep
interfaces sharp whilst maintaining the conservation properties of the system.
These algorithms are implemented in a highly-parallelised hierarchical adaptive
mesh refinement platform, and are verified and validated using numerical and
experimental benchmarks. Results indicate very good agreement with experiment
and an improvement of numerical performance compared to certain existing
Eulerian methods, without loss of conservation.
