Uniformly High-Order Structure-Preserving Discontinuous Galerkin Methods for Euler Equations with Gravitation: Positivity and Well-Balancedness

DOI10.1137/20M133782XzbMath1466.65150arXiv2005.07166MaRDI QIDQ5857621

Kailiang Wu, Yulong Xing

Publication date: 1 April 2021

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.07166

zbMATH Keywords

discontinuous Galerkin methodgravitational fieldcompressible Euler equationspositivity-preservingwell-balancedhyperbolic balance laws

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) First-order nonlinear hyperbolic equations (35L60) 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) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Euler equations (35Q31) Compressible Navier-Stokes equations (76N06)

Related Items (11)

Provably Positive Central Discontinuous Galerkin Schemes via Geometric Quasilinearization for Ideal MHD Equations ⋮ High-Order Positivity-Preserving Well-Balanced Discontinuous Galerkin Methods for Euler Equations with Gravitation on Unstructured Meshes ⋮ Positivity-preserving well-balanced central discontinuous Galerkin schemes for the Euler equations under gravitational fields ⋮ An efficient invariant-region-preserving central scheme for hyperbolic conservation laws ⋮ Well-balanced numerical method for atmospheric flow equations with gravity ⋮ High order structure-preserving arbitrary Lagrangian-Eulerian discontinuous Galerkin methods for the Euler equations under gravitational fields ⋮ On high order positivity-preserving well-balanced finite volume methods for the Euler equations with gravitation ⋮ Geometric Quasilinearization Framework for Analysis and Design of Bound-Preserving Schemes ⋮ Fifth-order well-balanced positivity-preserving finite difference AWENO scheme with hydrostatic reconstruction for hyperbolic chemotaxis models ⋮ High order well-balanced positivity-preserving scale-invariant AWENO scheme for Euler systems with gravitational field ⋮ High order structure-preserving finite difference WENO schemes for MHD equations with gravitation in all sonic Mach numbers

Uses Software

• HE-E1GODF

Cites Work

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