Adaptive hierarchic transformations for dynamically p-enriched slope-limiting over discontinuous Galerkin systems of generalized equations

  • Authors:

  • C. Michoski;C. Mirabito;C. Dawson;D. Wirasaet;E. J. Kubatko;J. J. Westerink

  • Affiliations:

  • Institute for Computational Engineering and Sciences (ICES), Computational Hydraulics Group (CHG), University of Texas, Austin, TX 78712, United States;Institute for Computational Engineering and Sciences (ICES), Computational Hydraulics Group (CHG), University of Texas, Austin, TX 78712, United States;Institute for Computational Engineering and Sciences (ICES), Computational Hydraulics Group (CHG), University of Texas, Austin, TX 78712, United States;Computational Hydraulics Laboratory, Department of Civil Engineering and Geological Sciences, University of Notre Dame, Notre Dame, IN 46556, United States;Department of Civil and Environmental Engineering and Geodetic Science, The Ohio State University, Columbus, OH 43210, United States;Computational Hydraulics Laboratory, Department of Civil Engineering and Geological Sciences, University of Notre Dame, Notre Dame, IN 46556, United States

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2011

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Abstract

We study a family of generalized slope limiters in two dimensions for Runge-Kutta discontinuous Galerkin (RKDG) solutions of advection-diffusion systems. We analyze the numerical behavior of these limiters applied to a pair of model problems, comparing the error of the approximate solutions, and discuss each limiter's advantages and disadvantages. We then introduce a series of coupled p-enrichment schemes that may be used as standalone dynamic p-enrichment strategies, or may be augmented via any in the family of variable-in-p slope limiters presented.