GENERIC-motivated extended symplectic numerical methods for dissipative mechanical systems: A concrete example and general messages

The GENERIC (General Equation for the Non-Equilibrium Reversible-Irreversible Coupling) framework is used, first, to present the irreversible thermodynamical formulation of the Rayleigh potential, and, subsequently, to realize the dynamical equations of motion of a supercritical van der Waals fluid separated from the environment by a movable rigid piston. Motivated by the latter, a quasi-symplectic generalization of the symplectic Euler finite-difference numerical scheme is introduced for this setup. A remarkable advantage over the explicit Euler scheme regarding artificial numerical antidissipation is illustrated. The possibility of controlled artificial numerical damping is addressed. The quasi-symplectic scheme is proven to enable efficient simulation of the considerably nonlinear and sensitive processes near the liquid-vapour critical point. A numerically feasible quantitative measure of nonlinearity of time-dependent processes is introduced and applied.