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Journal of Scientific Computing

Erschienen in:

26.04.2015

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

verfasst von: C. Michoski, C. Dawson, E. J. Kubatko, D. Wirasaet, S. Brus, J. J. Westerink

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2016

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Abstract

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.

Vorheriger Artikel A Novel Weakly-Intrusive Non-linear Multiresolution Framework for Uncertainty Quantification in Hyperbolic Partial Differential Equations

Nächster Artikel A Spectral Analysis of Subspace Enhanced Preconditioners

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Titel: A Comparison of Artificial Viscosity, Limiters, and Filters, for High Order Discontinuous Galerkin Solutions in Nonlinear Settings
verfasst von: C. Michoski
C. Dawson
E. J. Kubatko
D. Wirasaet
S. Brus
J. J. Westerink
Publikationsdatum: 26.04.2015
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2016
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-015-0027-2

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