Shock Regularization with Smoothness-Increasing Accuracy-Conserving Dirac-Delta Polynomial Kernels

B. W. Wissink, G. B. Jacobs (Corresponding Author), J. K. Ryan, W. S. Don, E. T.A. van der Weide

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
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Abstract

A smoothness-increasing accuracy conserving filtering approach to the regularization of discontinuities is presented for single domain spectral collocation approximations of hyperbolic conservation laws. The filter is based on convolution of a polynomial kernel that approximates a delta-sequence. The kernel combines a kth order smoothness with an arbitrary number of m zero moments. The zero moments ensure a mth order accurate approximation of the delta-sequence to the delta function. Through exact quadrature the projection error of the polynomial kernel on the spectral basis is ensured to be less than the moment error. A number of test cases on the advection equation, Burger’s equation and Euler equations in 1D and 2D show that the filter regularizes discontinuities while preserving high-order resolution away from a discontinuity.

Original languageEnglish
Pages (from-to)579-596
Number of pages18
JournalJournal of scientific computing
Volume77
Issue number1
Early online date30 Apr 2018
DOIs
Publication statusPublished - 1 Oct 2018

Fingerprint

Paul Adrien Maurice Dirac
Shock
Smoothness
Discontinuity
Regularization
Polynomials
kernel
Moment
Delta functions
Polynomial
Euler equations
Advection
Convolution
Filter
Advection Equation
Conservation
Hyperbolic Conservation Laws
Order of Approximation
Delta Function
Zero

Keywords

  • UT-Hybrid-D
  • Dirac-Delta
  • Filtering
  • Hyperbolic conservation laws
  • Regularization
  • Shock capturing
  • Chebyshev collocation

Cite this

Wissink, B. W. ; Jacobs, G. B. ; Ryan, J. K. ; Don, W. S. ; van der Weide, E. T.A. / Shock Regularization with Smoothness-Increasing Accuracy-Conserving Dirac-Delta Polynomial Kernels. In: Journal of scientific computing. 2018 ; Vol. 77, No. 1. pp. 579-596.
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Shock Regularization with Smoothness-Increasing Accuracy-Conserving Dirac-Delta Polynomial Kernels. / Wissink, B. W.; Jacobs, G. B. (Corresponding Author); Ryan, J. K.; Don, W. S.; van der Weide, E. T.A.

In: Journal of scientific computing, Vol. 77, No. 1, 01.10.2018, p. 579-596.

Research output: Contribution to journalArticleAcademicpeer-review

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