On limiting for higher order discontinuous Galerkin method for 2D Euler equations

  • Juan Pablo Gallego-Valencia
  • Christian Klingenberg
  • Praveen Chandrashekar
Article

DOI: 10.1007/s00574-016-0142-1

Cite this article as:
Gallego-Valencia, J.P., Klingenberg, C. & Chandrashekar, P. Bull Braz Math Soc, New Series (2016) 47: 335. doi:10.1007/s00574-016-0142-1

Abstract

We present an implementation of discontinuous Galerkin method for 2-D Euler equations on Cartesian meshes using tensor product Lagrange polynomials based on Gauss nodes. The scheme is stabilized by a version of the slope limiter which is adapted for tensor product basis functions together with a positivity preserving limiter. We also incorporate and test shock indicators to determine which cells need limiting. Several numerical results are presented to demonstrate that the proposed approach is capable of computing complex discontinuous flows in a stable and accurate fashion.

Keywords

partial differential equations conservation laws discontinuous Galerkin method limiters compressible Euler equations shock indicator 

Mathematical subject classification

35L65 

Copyright information

© Sociedade Brasileira de Matemática 2016

Authors and Affiliations

  • Juan Pablo Gallego-Valencia
    • 1
  • Christian Klingenberg
    • 1
  • Praveen Chandrashekar
    • 2
  1. 1.Dept. of MathematicsWürzburg UniversityWürzburgGermany
  2. 2.TIFR Center for Applicable MathematicsBangaloreIndia

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