Journal of Scientific Computing

, Volume 66, Issue 1, pp 406–434

A Comparison of Artificial Viscosity, Limiters, and Filters, for High Order Discontinuous Galerkin Solutions in Nonlinear Settings

  • C. Michoski
  • C. Dawson
  • E. J. Kubatko
  • D. Wirasaet
  • S. Brus
  • J. J. Westerink
Article

DOI: 10.1007/s10915-015-0027-2

Cite this article as:
Michoski, C., Dawson, C., Kubatko, E.J. et al. J Sci Comput (2016) 66: 406. doi:10.1007/s10915-015-0027-2
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Abstract

Nonlinear systems of equations demonstrate complicated regularity features that are often obfuscated by overly diffuse numerical methods. Using a discontinuous Galerkin finite element method, we study a nonlinear system of advection–diffusion–reaction equations and aspects of its regularity. For numerical regularization, we present a family of solutions consisting of: (1) a sharp, computationally efficient slope limiter, known as the BDS limiter, (2) a standard spectral filter, and (3) a novel artificial diffusion algorithm with a solution-dependent entropy sensor. We analyze these three numerical regularization methods on a classical test in order to test the strengths and weaknesses of each, and then benchmark the methods against a large application model.

Keywords

Discontinuous Galerkin Nonlinear system High order Regularization Slope limiting Spectral filters  Artificial diffusion Artificial viscosity Advection  Diffusion Reaction 

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • C. Michoski
    • 1
  • C. Dawson
    • 1
  • E. J. Kubatko
    • 2
  • D. Wirasaet
    • 3
  • S. Brus
    • 3
  • J. J. Westerink
    • 3
  1. 1.Institute for Computational Engineering and Sciences (ICES), Computational Hydraulics Group (CHG)University of Texas at AustinAustinUSA
  2. 2.Department of Civil and Environmental Enineering and Geodetic ScienceThe Ohio State UniversityColumbusUSA
  3. 3.Computational Hydraulics Laboratory, Department of Civil Engineering and Geological SciencesUniversity of Notre DameNotre DameUSA

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