Algorithms for coupled problems that preserve symmetries and the laws of thermodynamics: Part II: fractional step methods

This article proposes a new type of discretizations for initial boundary value problems of thermodynamical systems. Based on a combination of finite elements in space and fractional step methods in time, we formulate algorithms that exactly preserve the symmetries and the laws of thermodynamics of the continuum problem. The algorithmic design is based on the GENERIC formalism of irreversible thermodynamics which naturally suggests the split of the evolution operator upon which our fractional step method is based. Although the emphasis of the article is on the generality of the results, as an illustration, a discretization of nonlinear, finite strain, thermoelasticity is presented. Numerical simulations are provided that verify the excellent performance of the new methods.