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

DOI10.1016/j.amc.2022.127629OpenAlexW4309579157MaRDI QIDQ2101917

Saray Busto, Michael Dumbser, Remi Abgrall

Publication date: 7 December 2022

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2022.127629

zbMATH Keywords

entropy inequalityunified first order hyperbolic formulation of continuum mechanicsthermodynamically compatible finite volume schemeshyperbolic and thermodynamically compatible (HTC) systems with extra conservation lawnonlinear stability in the energy normthermodynamically compatible discontinuous Galerkin schemes

Mathematics Subject Classification ID

Basic methods in fluid mechanics (76Mxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Hyperbolic equations and hyperbolic systems (35Lxx)

Related Items (10)

Thermodynamically compatible discretization of a compressible two-fluid model with two entropy inequalities ⋮ Artificial viscosity to get both robustness and discrete entropy inequalities ⋮ A well-balanced and exactly divergence-free staggered semi-implicit hybrid finite volume / finite element scheme for the incompressible MHD equations ⋮ Relativistic constitutive modeling of inelastic deformation of continua moving in space-time ⋮ Linear quadratic optimal control for systems governed by first-order hyperbolic partial differential equations ⋮ On Thermodynamically Compatible Finite Volume Schemes for Overdetermined Hyperbolic Systems ⋮ An exactly curl-free staggered semi-implicit finite volume scheme for a first order hyperbolic model of viscous two-phase flows with surface tension ⋮ Preface for the special issue ``Hyperbolic PDE in computational physics: advanced mathematical models and structure-preserving numerics ⋮ A Personal Discussion on Conservation, and How to Formulate It ⋮ A new family of thermodynamically compatible discontinuous Galerkin methods for continuum mechanics and turbulent shallow water flows

Uses Software

• LIMbook

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