A new family of thermodynamically compatible discontinuous Galerkin methods for continuum mechanics and turbulent shallow water flows

DOI10.1007/s10915-022-02017-0zbMath1503.65223OpenAlexW4304092644MaRDI QIDQ2103425

Saray Busto, Michael Dumbser

Publication date: 13 December 2022

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-022-02017-0

zbMATH Keywords

cell entropy inequalityunsteady turbulent shallow water flowsnonlinear stability in the energy normthermodynamically compatible discontinuous Galerkin schemesthermodynamically compatible discretization of nonconservative hyperbolic PDEunified GPR model of continuum mechanics

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Nonlinear elasticity (74B20) Finite element methods applied to problems in solid mechanics (74S05) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Shear flows and turbulence (76F10) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Navier-Stokes equations (35Q30) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) PDEs in connection with classical thermodynamics and heat transfer (35Q79) Euler equations (35Q31) Diffusive and convective heat and mass transfer, heat flow (80A19) First-order hyperbolic equations (35L02) Compressible Navier-Stokes equations (76N06)

Uses Software

• LIMbook

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