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

作者：Michoski C^*; Dawson C; Kubatko E J; Wirasaet D; Brus S; Westerink J J

来源：Journal of Scientific Computing, 2016, 66(1): 406-434.

DOI：10.1007/s10915-015-0027-2

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

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.

• 出版日期2016-1