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  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. (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.

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 Creators:
Glaubitz, J.1, Author           
Nogueira, A. C., Author
Almeida, J. L. S., Author
Cantão, R. F., Author
Silva, C. A. C., Author
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Numerical Analysis
 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.

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Language(s): eng - English
 Dates: 2019
 Publication Status: Issued
 Pages: 24
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 Table of Contents: -
 Rev. Type: Peer
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Title: Journal of Scientific Computing
  Abbreviation : J. Sci. Comput.
Source Genre: Journal
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Publ. Info: Springer
Pages: - Volume / Issue: 79 (1) Sequence Number: - Start / End Page: 249 - 272 Identifier: -