SIAC Filtering for Nonlinear Hyperbolic Equations

Xiaozhou Li, Jennifer Ryan

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Abstract

We present the results of the symmetric and one-sided Smoothness-Increasing Accuracy-Conserving (SIAC) filter applied to a discontinuous Galerkin (DG) approximation for two examples of nonlinear hyperbolic conservation laws. The traditional symmetric SIAC filter relies on having a translation invariant mesh, periodic boundary conditions and linear equations. However, for practical applications that are modelled by nonlinear hyperbolic equations, this is not feasible. Instead we must concentrate on a filter that allows error reduction for nonuniform/unstructured meshes and non-periodic boundary conditions for nonlinear hyperbolic equations. This proceedings is an introductory exploration into the feasibility of these requirements for efficient filtering of nonlinear equations.
Original languageEnglish
Title of host publicationInterdisciplinary Topics in Applied Mathematics, Modeling and Computational Science
PublisherSpringer
Pages285-291
Volume117
Publication statusPublished - 4 Jul 2015

Publication series

NameSpringer Proceedings in Mathematics & Statistics
PublisherSpringer

Keywords

  • discontinuous Galerkin
  • hyperbolic equations
  • post-processing
  • nonlinear
  • SIAC filtering

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