Speaker
Description
The consistent numerical analysis of balance laws in multiphysical systems demands specialized time integration methods. These methods must respect the system’s invariants, as outlined by Noether’s theorem while adhering to key thermodynamic principles: conservation of linear and angular momentum, energy conservation, and positive dissipation. The GENERIC(General Equation for Non-Equilibrium Reversible-Irreversible Coupling) framework provides a foundation for creating such integrators in discrete systems. A thermo-visco-elastic pendulum undergoing large deformations is used as a model problem, featuring heat transfer and viscous dissipation—both of which pose challenges for numerical methods. Energy-Momentum-Entropy(EME) schemes, based on discrete gradients as proposed by Gonzalez [1], are developed for this model, demonstrating consistency with energy and entropy principles. The implications of selecting variables such as temperature, entropy, internal energy, or total energy as independent variables are explored. Special attention is given to a specific GENERIC formulation based on Mielke’s approach [2], as well as the introduction of auxiliary variables like strain and their impact on the discrete system’s structure. The model is extended to include electromagnetic forces, enabling the consistent simulation of coupled electro-mechanical and magneto-mechanical systems, which are essential in modern engineering. The development of GENERIC-based integrators for discrete systems represents an initial step towards applying these methods to continuum mechanics.
REFERENCES
[1] Gonzalez, O. Time integration and discrete Hamiltonian systems. Journal of NonLinearScience 6,449–467, (1996).
[2] Mielke, A. Formulation of thermoelastic dissipative material behavior using \linebreak GENERIC.Continuum Mechanics and Thermodynamics (2011).
