Volume 25, Issue 2
Central WENO Subcell Finite Volume Limiters for ADER Discontinuous Galerkin Schemes on Fixed and Moving Unstructured Meshes

Walter Boscheri, Matteo Semplice & Michael Dumbser

Commun. Comput. Phys., 25 (2019), pp. 311-346.

Published online: 2018-10

Preview Purchase PDF 185 5717
Export citation
  • Abstract

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.
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).

  • Keywords

Discontinuous Galerkin (DG) methods, high order ADER schemes, subcell finite volume limiter, central WENO reconstruction (CWENO), Arbitrary-Lagrangian-Eulerian schemes, moving unstructured meshes, hyperbolic conservation laws, Euler and MHD equations.

  • AMS Subject Headings

65Mxx, 65Zxx

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-25-311, author = {}, 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 = {

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.
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).

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0069}, url = {http://global-sci.org/intro/article_detail/cicp/12753.html} }
TY - JOUR T1 - Central WENO Subcell Finite Volume Limiters for ADER Discontinuous Galerkin Schemes on Fixed and Moving Unstructured Meshes JO - Communications in Computational Physics VL - 2 SP - 311 EP - 346 PY - 2018 DA - 2018/10 SN - 25 DO - http://doi.org/10.4208/cicp.OA-2018-0069 UR - https://global-sci.org/intro/article_detail/cicp/12753.html KW - Discontinuous Galerkin (DG) methods, high order ADER schemes, subcell finite volume limiter, central WENO reconstruction (CWENO), Arbitrary-Lagrangian-Eulerian schemes, moving unstructured meshes, hyperbolic conservation laws, Euler and MHD equations. AB -

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.
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).

Walter Boscheri, Matteo Semplice & Michael Dumbser. (2020). Central WENO Subcell Finite Volume Limiters for ADER Discontinuous Galerkin Schemes on Fixed and Moving Unstructured Meshes. Communications in Computational Physics. 25 (2). 311-346. doi:10.4208/cicp.OA-2018-0069
Copy to clipboard
The citation has been copied to your clipboard