article

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

Authors:

E. T. WeideAuthors Info & Claims

Journal of Scientific Computing, Volume 77, Issue 1

Pages 579 - 596

https://doi.org/10.1007/s10915-018-0719-5

Published: 01 October 2018 Publication History

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.

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Cited By

Bohm MSchermeng SWinters AGassner GJacobs G(2022)Multi-element SIAC Filter for Shock Capturing Applied to High-Order Discontinuous Galerkin Spectral Element MethodsJournal of Scientific Computing10.1007/s10915-019-01036-881:2(820-844)Online publication date: 11-Mar-2022
https://dl.acm.org/doi/10.1007/s10915-019-01036-8

Shock Regularization with Smoothness-Increasing Accuracy-Conserving Dirac-Delta Polynomial Kernels
1. Mathematics of computing
  1. Mathematical analysis
2. Theory of computation

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cover image Journal of Scientific Computing

Journal of Scientific Computing Volume 77, Issue 1

October 2018

688 pages

ISSN:0885-7474

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Copyright © Copyright © 2018 Springer Science+Business Media, LLC, part of Springer Nature.

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Plenum Press

United States

Publication History

Published: 01 October 2018

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Cited By

Bohm MSchermeng SWinters AGassner GJacobs G(2022)Multi-element SIAC Filter for Shock Capturing Applied to High-Order Discontinuous Galerkin Spectral Element MethodsJournal of Scientific Computing10.1007/s10915-019-01036-881:2(820-844)Online publication date: 11-Mar-2022
https://dl.acm.org/doi/10.1007/s10915-019-01036-8

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