Geometric integrators for adiabatically closed simple thermodynamic systems

TL;DR

This paper develops a discrete variational principle to create geometric numerical integrators for adiabatically closed simple thermodynamic systems, enhancing the simulation accuracy of their dynamics.

Contribution

It introduces a novel discrete variational framework for thermodynamic systems, enabling the construction of structure-preserving numerical integrators.

Findings

Numerical integrators accurately simulate thermodynamic dynamics.

The method preserves geometric structures inherent in thermodynamic systems.

Examples demonstrate the effectiveness of the proposed integrators.

Abstract

A variational formulation for non-equilibrium thermodynamics was developed by Gay-Balmaz and Yoshimura. In a recent article, the first two authors of the present paper introduced partially cosymplectic structures as a geometric framework for thermodynamic systems, recovering the evolution equations obtained variationally. In this paper, we develop a discrete variational principle for adiabatically closed simple thermodynamic systems, which can be utilised to construct numerical integrators for the dynamics of such systems. The effectiveness of our method is illustrated with several examples.