@Article{CiCP-25-311,
author = {Walter Boscheri, Matteo Semplice and Michael Dumbser},
title = {Central WENO Subcell Finite Volume Limiters for ADER Discontinuous Galerkin Schemes on Fixed and Moving Unstructured Meshes},
journal = {Communications in Computational Physics},
year = {2018},
volume = {25},
number = {2},
pages = {311--346},
abstract = {<p style="text-align: justify;">We present a novel a posteriori subcell finite volume limiter for high order
discontinuous Galerkin (DG) finite element schemes for the solution of nonlinear hyperbolic
PDE systems in multiple space dimensions on fixed and moving unstructured
simplex meshes. The numerical method belongs to the family of high order fully discrete
one-step ADER-DG schemes [12, 45] and makes use of an element-local space-time
Galerkin finite element predictor. Our limiter is based on the MOOD paradigm, in
which the discrete solution of the high order DG scheme is checked a posteriori against
a set of physical and numerical admissibility criteria, in order to detect spurious oscillations
or unphysical solutions and in order to identify the so-called troubled cells.
Within the detected troubled cells the discrete solution is then discarded and recomputed
locally with a more robust finite volume method on a fine subgrid.<br/>In this work, we propose for the first time to use a high order ADER-CWENO finite
volume scheme as subcell finite volume limiter on unstructured simplex meshes, instead
of a classical second order TVD scheme. Our new numerical scheme has been
developed both for fixed Eulerian meshes as well as for moving Lagrangian grids. It
has been carefully validated against a set of typical benchmark problems for the compressible
Euler equations of gas dynamics and for the equations of ideal magnetohydrodynamics
(MHD).</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2018-0069},
url = {http://global-sci.org/intro/article_detail/cicp/12753.html}
}