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Geometric Mechanics Formulations and Structure-Preserving Discretizations for Continuum Mechanics

Christopher Eldred, Sandia National Laboratories
Anthony Gruber, Sandia National Laboratories
Artur PalhaDelft University of Technology

Continuum mechanics has an elegant description in terms of geometric mechanics formulations (variational, Hamiltonian, metriplectic, GENERIC, port-Hamiltonian, etc.). These geometric descriptions enable the accurate representation of both reversible (thermodynamic entropy-conserving) and irreversible (thermodynamic entropy-generating) dynamics, and for the correct interconnection/coupling between systems. By emulating the fundamental features of these geometric formulations in a numerical model (i.e., a structure-preserving discretization), many desirable properties can be obtained, e.g., freedom from spurious/unphysical numerical modes, consistent energetics, controlled dissipation of enstrophy or thermodynamic entropy, and stable coupling between systems. Examples of this include spatial, temporal and spatiotemporal discretizations such as compatible Galerkin methods, symplectic integrators, and discrete exterior calculus. This minisymposium brings together researchers studying and implementing these ideas at both the continuous and discrete levels across a wide range of continuum mechanics models, including geophysical fluid dynamics, plasma, compressible flow, and solid mechanics.