Generic based thermodynamically consistent discretisation in spaceand time for open thermomechanical systems

Abstract

In the present contribution structure-preserving numerical methods for finite strain thermoelastodynamics are proposed. The underlying variational formulation is based on the GENERIC formalism and makes possible the free choice of the thermodynamic state variable. The notion ‘GENERIC consistent space discretization’ is introduced which facilitates the design of Energy-Momentum-Entropy (EME) consistent schemes. In particular, three alternative EME schemes result from the present approach. These schemes are directly linked to the respective choice of the thermodynamic variable. A numerical example confirms the structure-preserving properties of the newly developed EME schemes, which exhibit superior numerical stability.