A first order conservation law framework for fast solid dynamics: Smooth particle hydrodynamics

This paper presents a novel Smooth Particle Hydrodynamics computational framework for the simulation of large strain fast solid dynamics in thermo-elasticity, with a tailor-made implementation into the modern CFD open source package “OpenFOAM”. The formulation is based on the Total Lagrangian description of a system of first order conservation laws written in terms of the linear momentum, the deformation gradient tensor and the total energy of the system. To ensure the stability (i.e. hyperbolicity) of the formulation from the continuum point of view, a well-posed internal energy density is expressed as a combination of the deformation measure and the entropy density. Moreover, and to guarantee stability from the spatial discretisation point of view, consistently derived Riemann-based numerical dissipation is carefully introduced where global numerical entropy production is demonstrated via a novel technique in terms of the time rate of the so-called ballistic free energy of the system. A series of numerical examples is presented in order to assess the applicability and robustness of the proposed formulations, where the Smooth Particle Hydrodynamics scheme is benchmarked against an alternative in-house Vertex Centred Finite Volume implementation