Runge-Kutta discontinuous Galerkin method using WENO limiters II: Unstructured meshes

DOI10.1016/j.jcp.2007.12.024zbMath1157.65453OpenAlexW2003988341MaRDI QIDQ924436

Jianxian Qiu, Michael Dumbser, Chi-Wang Shu, Jun Zhu

Publication date: 16 May 2008

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2007.12.024

zbMATH Keywords

limitershigh order accuracyRunge-Kutta discontinuous Galerkin methodWENO finite volume scheme

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99)

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Cites Work

• Unnamed Item
• Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method. II: Two dimensional case
• Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems
• The numerical simulation of two-dimensional fluid flow with strong shocks
• Uniformly high order accurate essentially non-oscillatory schemes. III
• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• Efficient implementation of essentially nonoscillatory shock-capturing schemes. II
• TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
• Weighted essentially non-oscillatory schemes on triangular meshes
• The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
• Parallel, adaptive finite element methods for conservation laws
• Weighted essentially non-oscillatory schemes
• Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method: One-dimensional case.
• Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
• Weighted essentially non-oscillatory schemes for the interpolation of mean values on unstructured grids
• On the construction, comparison, and local characteristic decomposition for high-order central WENO schemes
• Efficient implementation of weighted ENO schemes
• A Hermite WENO-based limiter for discontinuous Galerkin method on unstructured grids
• Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems
• The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws
• The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
• TVB Uniformly High-Order Schemes for Conservation Laws
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• Central WENO schemes for hyperbolic systems of conservation laws
• Runge--Kutta Discontinuous Galerkin Method Using WENO Limiters
• A problem-independent limiter for high-order Runge-Kutta discontinuous Galerkin methods
• A technique of treating negative weights in WENO schemes

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