An interface-capturing Godunov method for the simulation of compressible solid-fluid problems

Abstract

In this paper a new three-dimensional Eulerian interface-capturing model is proposed for the simulation of compressible solid-fluid problems. The model is a development of a well-established five equation multi-fluid model to include material strength, by incorporating a new kinematic evolution equation for the elastic stretch tensor, and augmenting the Mie-Grüneisen equation-of-state to include a contribution from elastic strain. Principal to the development of the model is the fact that a great number of solid materials can be described by the particular general equation-of-state framework, which reduces to the Mie-Grüneisen equation-of-state in the limit of zero strength and is thus equally applicable to a wide class of fluids. The constitutive models are founded on hyperelastic theory and are therefore thermodynamically compatible. Only one kinematic equation is required for arbitrary numbers of components by assuming that mixtures are described by a common deviatoric strain tensor. The system of evolution equations can be written in conservation law form, and are therefore suitable for application of Godunov's method; specifically an HLLD Riemann solver is formulated for the calculation of numerical fluxes. Interfaces are sharpened by using the THINC method in conjunction with MUSCL reconstruction. A time operator splitting strategy is used to divide the time integration into an explicit elastic update, which uses the third order TVD Runge-Kutta method, followed by an implicit plastic update. The method is verified using a number of challenging solid-fluid problems, including a high-velocity impact of a viscoplastic strain-hardening cylinder in air. The potential of the model for practical problems is demonstrated through three-dimensional simulation of an explosive buried in solid ground material.