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