A unified multi-physics formulation for combustion modelling

The motivation of this work is to produce an integrated mathematical formulation for the numerical modelling of material response due to detonation wave loading. In particular, we are interested to capture miscible and immiscible behaviour within condensed-phase explosives arising from the co-existence of a reactive carrier mixture of miscible materials, and several material interfaces due to the presence of immiscible impurities such as particles or cavities. The dynamic and thermodynamic evolution of the explosive is communicated to one or more inert confiners through their shared interfaces, which may undergo severe topological change. We also wish to consider elastic and plastic structural response of the confiners, rather than make a hydrodynamic assumption for their behaviour. Recently developed methodologies meet these requirements by means of the simultaneous solution of appropriate systems of equations for the behaviour of the condensed-phase explosive and the elastoplastic response of the confiners. In the present work, we employ a mathematical model proposed by Peshkov and Romenski, which unifies fluid and solid mechanics by means of generalising the concept of distortion tensors beyond solids. We amalgamate this model with a single system of partial differential equations (PDEs) which meets the requirement of co- existing miscible and immiscible explosive mixtures. We present the mathematical derivation of our unified model and construct appropriate algorithms for its solution. The model is extensively verified and validated against exact numerical or analytical solutions and available experimental results. To enable the application of the model to a wider range of problems, we consider two further extensions. The first addresses the extension to multiple inert or reactive materials and its assessment on realistic scenarios like the mechanical sensitisation of liquid explosives. The second is concerned with the use of hyperbolic thermal impulse equations to model the conduction of heat across material interfaces. This is assessed in the scenario of thermal-induced ignition and transition to detonation in explosives. Results of this work indicate that the developed formulation provides a powerful alternative to existing combustion models, able to seamlessly account for the complex and highly non-linear multi-material interactions present in combustion applications.