Work

GENERIC-Motivated Extended Symplectic Numerical Methods for Dissipative Mechanical Systems: A Concrete Example and General Messages

Year: 2025

Type: article

Abstract: 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.

Source: Journal of Computational and Applied Mechanics

DOI: 10.32973/jcam.2025.001

Authors: Tamás Fülöp, Mátyás Szücs, Donát M. Takács

Institutions: Budapest University of Technology and Economics, Institute for Particle and Nuclear Physics, HUN-REN Wigner Research Centre for Physics, Montavid Thermodynamic Research Group

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Magyar Tudományos Akadémia, Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, National Research, Development and Innovation Office

Awards: G2009994475, G2043034707, G467405575, G626611521, G739158750