Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws

By Lilia Krivodonova, J. Xin, Jean-François Remacle, Nicolas Chevaugeon, Joseph E. Flaherty. 2004

494 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/8a95d38e9b78999595e513fa1c4fa587b672be20

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

Citations in the corpus

A high‐order triangular discontinuous Galerkin oceanic shallow water model (2008, background): “discontinuity detector presented in [32].”
An adaptive discretization of shallow‐water equations based on discontinuous Galerkin methods (2006, background): “A complete description of the test case and of the available experimental data can be found in Reference [25].”
A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws (2014, background): “Originally, slope limiters were developed to constrain piecewise linear polynomial reconstructions based on a discrete maximum principle, therefore constructing “slope” limiters for higher order polynomials are difficult to build into this paradigm [69, 76].”
Discontinuous Galerkin Method for Time-Dependent Problems: Survey and Recent Developments (2014, background): “In practice, the TVB indicator [79] and the KXRCF indicator [55] are often the best choices.”
A Parameter-Free Generalized Moment Limiter for High- Order Methods on Unstructured Grids (2009, background): “named KXRCF in [19], and the Harten [11] marker are the best three among the seven markers they studied based on the amount of spurious oscillations in the solution, and the total number of cells marked.”
Superconvergence of discontinuous Galerkin solutions for a nonlinear scalar hyperbolic problem (2006, background): “We note that reliable shock detection is key to successful adaptive limiting strategies [23].”
Runge-Kutta Discontinuous Galerkin Method with a Simple and Compact Hermite WENO Limiter (2016, methodology): “Assuming △0 is the troubled cell detected by the KXRCF technique [18] by using (2.”
A well‐balanced Runge–Kutta discontinuous Galerkin method for the shallow‐water equations with flooding and drying (2008, methodology): “The motivation for using the above detection criterion stems from the observation that smooth DG solutions often exhibit a superconvergence behavior at outflow boundaries of mesh cells; we refer to [40] and references therein for more details.”