A simple and general framework for the construction of thermodynamically compatible schemes for computational fluid and solid mechanics

Rémi Abgrall, Saray Busto and Michael Dumbser

Applied Mathematics and Computation, 2023, vol. 440, issue C

Abstract: We introduce a simple and general framework for the construction of thermodynamically compatible schemes for the numerical solution of overdetermined hyperbolic PDE systems that satisfy an extra conservation law. As a particular example in this paper, we consider the general Godunov-Peshkov-Romenski (GPR) model of continuum mechanics that describes the dynamics of nonlinear solids and viscous fluids in one single unified mathematical formalism.

Keywords: Hyperbolic and thermodynamically compatible (HTC) systems with extra conservation law; Entropy inequality; Nonlinear stability in the energy norm; Thermodynamically compatible finite volume schemes; Thermodynamically compatible discontinuous Galerkin schemes; Unified first order hyperbolic formulation of continuum mechanics (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:440:y:2023:i:c:s0096300322007020

DOI: 10.1016/j.amc.2022.127629

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