Smooth and compactly supported viscous sub-cell shock capturing for 
Discontinuous Galerkin methods

Glaubitz, J.; Nogueira, A. C.; Almeida, J. L. S.; Cantão, R. F.; Silva, C. A. C.

doi:10.1007/s10915-018-0850-3

Item

ITEM ACTIONSEXPORT

Add to Basket

Local TagsRelease HistoryDetailsSummary

Released

Journal Article

Smooth and compactly supported viscous sub-cell shock capturing for Discontinuous Galerkin methods

MPS-Authors

/persons/resource/persons240651

Glaubitz, J.
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.1007/s10915-018-0850-3
(Publisher version)

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

Fulltext (public)

arXiv:1810.02152.pdf
(Preprint), 827KB

Supplementary Material (public)

There is no public supplementary material available

Citation

Glaubitz, J., Nogueira, A. C., Almeida, J. L. S., Cantão, R. F., & Silva, C. A. C. (2019). Smooth and compactly supported viscous sub-cell shock capturing for Discontinuous Galerkin methods. Journal of Scientific Computing, 79(1), 249-272. doi:10.1007/s10915-018-0850-3.

Cite as: https://hdl.handle.net/21.11116/0000-0004-83D1-B

Abstract

In this work, a novel artificial viscosity method is proposed using smooth and compactly supported viscosities. These are derived by revisiting the widely used piecewise constant artificial viscosity method of Persson and Peraire as well as the piecewise linear refinement of Klöckner et al. with respect to the fundamental design criteria of conservation and entropy stability. Further investigating the method of modal filtering in the process, it is demonstrated
that this strategy has inherent shortcomings, which are related to problems of Legendre viscosities to handle shocks near element boundaries. This problem is overcome by introducing certain functions from the fields of robust reprojection and mollififers as viscosity distributions. To the best of our
knowledge, this is proposed for the first time in this work. The resulting $C_0^\infty$ artificial viscosity method is demonstrated to provide sharper profiles, steeper gradients and a higher resolution of small-scale features while still maintaining stability of the method.