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

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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

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    Keywords

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

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