A cell-centered Lagrangian Godunov-like method for solid dynamics

This work presents a spatially and temporally second-order cell-centered Lagrangian formulation (CCH) suitable for elasto-plastic materials on unstructured polyhedral cells in multiple dimensions. In the development of our scheme, we follow a mimetic approach, based upon the finite volume method, as a guide to the derivation of the difference equations. In doing so, we consider not only the governing equations, but a number of ancillary relationships. The finite volume equations for solids are cast in Lagrangian form with particular attention to the discrete form of the Second Law of Thermodynamics. We expand upon previous work and propose a new entropy production expression. A new tensor dissipation model is presented that guarantees the viscous stress tensor is symmetric. The new tensor dissipation model shows increased mesh robustness. In the second-order formulation, a limiter for the stress gradient is presented, as well as a vorticity limiter for the velocity gradient. Numerical results are demonstrated for common test problems involving both gas and solid constitutive models.