A new framework for the computational simulation of problems arising in continuum me- chanics is presented. It is unified in the sense that it can describe all three major phases of matter within the same set of equations. It is able to represent inviscid fluids, Newtonian and non-Newtonian viscous fluids, elastic and plastic solids, and reactive species. These materials are presented with a variety of equations of state, and there is a clear methodology for extending the framework to more exotic materials using other constitutive equations. It is capable of accurately modeling interfaces between regions occupied by different phases, and by the vacuum.

The problem of impact-induced detonation in an elastoplastic confiner is one that incorpo- rates the whole range of aforementioned material types, representing a challenge to existing frameworks. This new framework is shown to accurately and efficiently solve this problem.

The framework comprises a modification and extension of the Godunov-Peshkov-Romenski (GPR) model of continuum mechanics, along with a new set of operator-splitting-based numerical solvers to allow for the efficient solution of the problems that it is put to, and a new Riemann ghost fluid method for accurate simulation of material interfaces. In addition to this work, novel mathematical analyses of the structure of the GPR equations - and the numerical methods currently used to solve them - are presented in this study.

This new framework presents a range of benefits: the conceptual work required to implement a computational simulation involving many different components is greatly reduced, saving time and allowing for greater specialization of computational techniques. This has the po- tential to streamline development of simulation software by reducing the number of different systems of equations that require solvers, and cutting down on the amount of theoretical work required, for example in the treatment of interfaces in multimaterial problems.