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,

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... 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.