Runge-Kutta Discontinuous Galerkin Method Using WENO Limiters

By Jianxian Qiu, Chi-Wang Shu. SIAM Journal on Scientific Computing, 2005

464 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/fc5c0463e2baafd55492563e0af306c78aa74fb2

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

A set of parallel, implicit methods for a reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids (2014, unknown): “Introduction The discontinuous Galerkin (DG) methods [1–26] have recently become popular for the solution of systems of conservation laws.”
A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws (2014, methodology): “However, amongst all DG limiters, three families seem to emerge: artificial viscosity based limiters such as [87, 79, 48, 78, 106, 107, 20, 45, 34, 44], “Slope” or moment limiters, for instance the total variation bounded (TVB) limiter of Cockburn and Shu [26, 25, 24, 22], the moment-based limiters ”
Discontinuous Galerkin Method for Time-Dependent Problems: Survey and Recent Developments (2014, background): “Qiu and Shu [70] and Zhu et al.”
Non-Oscillatory Hierarchical Reconstruction for Central and Finite Volume Schemes (2006, methodology): “In Qiu and Shu [32, 33], the WENO and Hermite WENO reconstructions are developed as limiters for DG.”
Runge-Kutta Discontinuous Galerkin Method with a Simple and Compact Hermite WENO Limiter (2016, methodology): “This type of limiters includes the WENO limiter [23, 32] and the HWENO limiter [21, 22, 25], which use the classical WENO finite volume methodology for reconstruction and thus require a wide stencil, especially for higher order methods.”
High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems (2009, unknown): “This approach has been pursued in [127, 126, 129].”
A Parameter-Free Generalized Moment Limiter for High- Order Methods on Unstructured Grids (2009, methodology): “24Luo, H., Baum, J.D., and Lo¨hner, R., “A Hermite WENO-based limiter for discontinuous Galerkin method on unstructured grids,” J. Comput.”
Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems (2007, methodology): “The initial condition for the system is zero except of the first component (density fluctuation q) which is given according to Jiang and Shu [25] as qðx; 0Þ ¼ 1 6 ½Gðx; z dÞ þ Gðx; zþ dÞ þ 4Gðx; zÞ ; 0:8 6 x 6 0:6; 1; 0:4 6 x 6 0:2; 1 j10 x 0:1ð Þj; 0:0 6 x 6 0:2; 1 6 ½F ðx; a dÞ þ F ðx; aþ dÞ þ 4F ”
Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method: one-dimensional case (2004, methodology): “In Section 3, we investigate the usage of the HWENO finite volume methodology as limiters for RKDG methods, following the idea in [ 22 ], with the goal of obtaining a robust and high order limiting procedure to simultaneously obtain uniform high order accuracy and sharp, non-oscillatory shock transi”