A problem-independent limiter for high-order Runge—Kutta discontinuous Galerkin methods

By A. Burbeau, Pierre Sagaut, Charles-Henri Bruneau. 2001

258 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/69c2597db7fd636ad8af9235fd79e9c1b690733b

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In Computational Mechanics

Citations in the corpus

A triangular spectral/hp discontinuous Galerkin method for modelling 2D shallow water equations (2004, background): “Now, we can write the limited solution in T0 as hU1 = (Ũ00 + ̃̃ U00) 00 + ̃̃ U01 01 + ̃̃ U10 10 (38) where [10]”
Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids. Basic Formulation (2002, background): “Other limiters, such as the problem independent limiter developed in [8], will be considered in a future publication.”
Runge-Kutta Discontinuous Galerkin Method with a Simple and Compact Hermite WENO Limiter (2016, methodology): “Many limiters have been studied in the literature for RKDG methods, such as the minmod type total variation bounded (TVB) limiter [5, 6, 7, 8], the moment based limiter [2] and an improved moment limiter [3] and so on.”
Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids (2002, methodology): “Note that with a special choice of basis functions, it is possible to achieve a diagonal mass matrix in the DG method, e.g., [ 8 ].”
The discontinuous Galerkin method with Lax-Wendroff type time discretizations (2005, background): “[9,8,7,6,10,1,4], they tend to degenerate accuracy when mistakenly used in smooth regions of the solution.”
Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method: one-dimensional case (2004, background): “The computational domain for this problem is [0,4] · [0,1].”
A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws (2014, methodology): “”Slope”/moment reduction Slope limiting or moment reduction techniques may permit to control the jumps of the DG polynomials by constraining or nullifying the high-order components in designated cells [12, 1, 27, 75, 115].”
Runge-Kutta Discontinuous Galerkin Method Using WENO Limiters (2005, background): “Many such limiters exist in the literature; for example, the minmod-type limiters in [9, 8, 7, 5, 10], the moment-based limiters in [2], and the more recent limiter in [3].”
Space--time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows: I. general formulation (2002, background): “[7] proposed limiters for second- and higher-order-accurate DG methods without problem-dependent constants which look promising, but they still need further testing on real applications.”