Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method II: Two dimensional case

By Jianxian Qiu, Chi-Wang Shu. 2005

332 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/e1027045b37f755b711764feeece84c0014f9bea

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

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.”
Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method: one-dimensional case (2004, methodology): “In [22], we constructed a class of fifth-order weighted essentially non-oscillatory (WENO) schemes based on Hermite polynomials, termed HWENO (Hermite WENO) schemes, for solving one dimensional non-linear hyperbolic conservation law systems, and applied this HWENO finite volume methodology as limite”
Runge-Kutta Discontinuous Galerkin Method with a Simple and Compact Hermite WENO Limiter (2016, unknown): “Email addresses: zhujun@nuaa.edu.cn (J. Zhu), zhongxh@math.msu.edu (X. Zhong), shu@dam.brown.edu (C.-W. Shu), jxqiu@xmu.edu.cn (J. Qiu) http://www.global-sci.com/ 1 c©201x Global-Science Press”
Hermite WENO schemes for Hamilton-Jacobi equations (2005, unknown): “In [23,24] we presented a class of WENO schemes based on Hermite polynomials, termed HWENO schemes, for solving one and two dimensional nonlinear hyperbolic conservation law systems.”
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): “The effort in [68, 71] attempts to construct Hermite type WENO approximations, which use the information of not only the cell averages but also the lower order moments such as slopes, to reduce the spread of reconstruction stencils.”
A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes (2008, methodology): “…of reconstruction operators are also applied to DG schemes in order to serve as limiters, as in the HWENO Email addresses: michael.dumbser@ing.unitn.it (Michael Dumbser), dbalsara@nd.edu (Dinshaw Balsara), toro@ing.unitn.it (Eleuterio F. Toro), munz@iag.uni-stuttgart.de (Claus-Dieter Munz).”
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 ”
High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems (2009, methodology): “The Hermite WENO schemes designed in [133, 136, 137] evolve a linear function per cell (hence they evolve two pieces of information per cell in one dimension) and reconstruct the necessary point values to higher order accuracy when necessary.”