A new troubled-cell indicator for discontinuous Galerkin methods for hyperbolic conservation laws

We introduce a new troubled-cell indicator for the discontinuous Galerkin (DG) methods for solving hyperbolic conservation laws. This indicator can be defined on unstructured meshes for high order DG methods and depends only on data from the target cell and its immediate neighbors. It is able to ide...

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Bibliographic Details
Published in:Journal of computational physics 2017-10, Vol.347, p.305-327
Main Authors: Fu, Guosheng, Shu, Chi-Wang
Format: Article
Language:English
Subjects:
Computational physics
Conservation laws
Discontinuous Galerkin method
Euler-Lagrange equation
Galerkin method
High order accuracy
Hyperbolic systems
Limiters
Parameter estimation
Parameter identification
Parameter sensitivity
Runge-Kutta method
Sensitivity analysis
Simulation
Troubled-cell indicator
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Summary:We introduce a new troubled-cell indicator for the discontinuous Galerkin (DG) methods for solving hyperbolic conservation laws. This indicator can be defined on unstructured meshes for high order DG methods and depends only on data from the target cell and its immediate neighbors. It is able to identify shocks without PDE sensitive parameters to tune. Extensive one- and two-dimensional simulations on the hyperbolic systems of Euler equations indicate the good performance of this new troubled-cell indicator coupled with a simple minmod-type TVD limiter for the Runge–Kutta DG (RKDG) methods.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2017.06.046