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

By Jianxian Qiu, Chi-Wang Shu. 2004

486 citations recorded by the source corpus.

Subfields: Atmospheric Science, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/a5e1df8a19f9d5aa45bd66c6c3171337ac874c2a

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Citations in the corpus

The discontinuous Galerkin method with Lax-Wendroff type time discretizations (2005, methodology): “In this paper we adopt the WENO limiter developed in [21] for k = 1 and HWENO limiter in [22,23] for k = 2 to maintain the compactness of the DG method.”
Analysis and numerical investigation of two dynamic models for liquid chromatography (2013, methodology): “The scheme can be easily extended to higher orders by using high order basis functions and by employing better slope limiters, for example reconstruction with the WENO limiters [69].”
A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes (2008, methodology): “In the general case, the PNPM reconstruction leads to very compact stencils, as for HWENO schemes [58,59,5], hence we can admit this quite generous choice for the stencil size.”
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.”
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.”
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.”
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, 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.”
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 ”
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 Robust WENO Type Finite Volume Solver for Steady Euler Equations on Unstructured Grids (2011, methodology): “In [26], a Hermite WENO scheme is proposed for the one-dimensional problems, and it is used as limiters for Runge-Kutta discontinuous Galerkin method.”