High-order entropy stable discontinuous Galerkin methods for the shallow water equations: curved triangular meshes and GPU acceleration

DOI10.1016/j.camwa.2020.11.006OpenAlexW3110404657MaRDI QIDQ2226776

Xinhui Wu, Jesse Chan, Ethan J. Kubatko

Publication date: 9 February 2021

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.02516

zbMATH Keywords

shallow water equationshigh orderdiscontinuous Galerkinentropy stabilityGPUssummation by parts

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Hyperbolic conservation laws (35L65) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (10)

A stable space-time FE method for the shallow water equations ⋮ Entropy stable modal discontinuous Galerkin schemes and wall boundary conditions for the compressible Navier-Stokes equations ⋮ A high-order velocity-based discontinuous Galerkin scheme for the shallow water equations: local conservation, entropy stability, well-balanced property, and positivity preservation ⋮ A class of structurally complete approximate Riemann solvers for trans- and supercritical flows with large gradients ⋮ A well-balanced weighted compact nonlinear scheme for shallow water equations on curvilinear grids ⋮ Provably stable flux reconstruction high-order methods on curvilinear elements ⋮ A positivity preserving strategy for entropy stable discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations ⋮ SUPG formulation augmented with YZβ shock‐capturing for computing shallow‐water equations ⋮ An entropy stable discontinuous Galerkin method for the two-layer shallow water equations on curvilinear meshes ⋮ An arbitrary high order well-balanced ADER-DG numerical scheme for the multilayer shallow-water model with variable density

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