Simulation of wave and front propagation in thermoelastic materials with phase transformation

A thermodynamically consistent form for the finite-volume numerical method for thermoelastic wave and front propagation is proposed in the paper. Such a reformulation provides the applicability of the Godunov type numerical schemes based on averages of field variables to the description of non-equilibrium situations. The non-equilibrium description is fulfilled by using contact quantities instead of numerical fluxes. The contact quantities satisfy the thermodynamic consistency conditions at interfaces which generalize the classical equilibrium conditions.