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Adaptive hierarchic transformations for dynamically p-enriched slope-limiting over discontinuous Galerkin systems of generalized equations |
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| Authors: | C. Michoski C. Mirabito C. Dawson D. Wirasaet E.J. Kubatko J.J. Westerink |
| Affiliation: | 1. Institute for Computational Engineering and Sciences (ICES), Computational Hydraulics Group (CHG), University of Texas, Austin, TX 78712, United States;2. Computational Hydraulics Laboratory, Department of Civil Engineering and Geological Sciences, University of Notre Dame, Notre Dame, IN 46556, United States;3. Department of Civil and Environmental Engineering and Geodetic Science, The Ohio State University, Columbus, OH 43210, United States |
| 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. |
| Keywords: | Discontinuous Galerkin Finite element RKDG Strong stability preserving (SSP) Total variation diminishing (TVD) Adaptive slope limiting Shock capturing Dynamic p-adaptivity Dynamic p-enrichment Error analysis Advective transport Hyperbolic PDE |
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