A cell-centered implicit-explicit Lagrangian scheme for a unified model of nonlinear continuum mechanics on unstructured meshes

A cell-centered implicit-explicit updated Lagrangian finite volume scheme on unstructured grids is proposed for a unified first order hyperbolic formulation of continuum fluid and solid mechanics. The provably respects the stiff relaxation limits continuous model at fully discrete level, thus it asymptotic preserving. Furthermore, GCL satisfied by compatible discretization that makes use nodal solver to compute vertex-based fluxes are used both motion computational mesh as well time evolution governing PDEs. Second-order accuracy in space achieved using TVD piecewise linear reconstruction, while an (IMEX) Runge-Kutta allows obtain higher also time. Particular care devoted design ODE solver, based approximate analytical solutions equations, plays crucial role when visco-plastic limit approached. We demonstrate robustness wide spectrum material responses covered includes inviscid hydrodynamics, viscous heat conducting fluids, elastic elasto-plastic solids multidimensional settings.