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

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    2 Citations (Scopus)
    18 Downloads (Pure)

    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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