A Comparison of Artificial Viscosity, Limiters, and Filters, for High Order Discontinuous Galerkin Solutions in Nonlinear Settings
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- 作者：C. Michoski ; C. Dawson ; E. J. Kubatko ; D. Wirasaet…
- 关键词：Discontinuous Galerkin ; Nonlinear system ; High order ; Regularization ; Slope limiting ; Spectral filters ; Artificial diffusion ; Artificial viscosity ; Advection ; Diffusion ; Reaction
- 刊名：Journal of Scientific Computing
- 出版年：2016
- 出版时间：January 2016
- 年：2016
- 卷：66
- 期：1
- 页码：406-434
- 全文大小：29,006 KB
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53.Zingan, V.N.: Discontinuous Galerkin finite element method for the nonlinear hyperbolic problems with entropy-based artificial viscosity stabilization. Dissertation, Texas A&M University (2012) - 作者单位：C. Michoski (1)
C. Dawson (1)
E. J. Kubatko (2)
D. Wirasaet (3)
S. Brus (3)
J. J. Westerink (3)
1. Institute for Computational Engineering and Sciences (ICES), Computational Hydraulics Group (CHG), University of Texas at Austin, Austin, TX, 78712, USA
2. Department of Civil and Environmental Enineering and Geodetic Science, The Ohio State University, Columbus, OH, 43210, USA
3. Computational Hydraulics Laboratory, Department of Civil Engineering and Geological Sciences, University of Notre Dame, Notre Dame, IN, 46556, USA - 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Algorithms
Computational Mathematics and Numerical Analysis
Applied Mathematics and Computational Methods of Engineering
Mathematical and Computational Physics - 出版者：Springer Netherlands
- ISSN：1573-7691
文摘
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