Shock Regularization with Smoothness-Increasing Accuracy-Conserving Dirac-Delta Polynomial Kernels
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 order smoothness with an arbitrary number of zero moments. The zero moments ensure a 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 shown that the filter regularizes discontinuities while preserving high-order resolution
Cite
@article{arxiv.1708.07156,
title = {Shock Regularization with Smoothness-Increasing Accuracy-Conserving Dirac-Delta Polynomial Kernels},
author = {B. W. Wissink and G. B. Jacobs and J. K. Ryan and W. S. Don and E. T. A. van der Weide},
journal= {arXiv preprint arXiv:1708.07156},
year = {2026}
}