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gPC for the Euler Equations

  • Mass Per Pettersson
  • Gianluca Iaccarino
  • Jan Nordström
Chapter
  • 2k Downloads
Part of the Mathematical Engineering book series (MATHENGIN)

Abstract

We present a stochastic Galerkin formulation of the Euler equations based on the variables introduced by P. L. Roe in 1981 for the well-known and widely used Roe solver. For numerical discretization, a Roe average matrix for the standard MUSCL-Roe scheme with Roe variables is derived. The Roe variable formulation is robust for supersonic problems where failure occurs for the standard implementation based on the conservative variable formulation. The robustness properties can be significantly improved with a stochastic basis that admits an eigenvalue decomposition with constant eigenvectors of the inner triple product matrix that occur frequently in the evaluation of pseudospectral operations. When this is the case, the Roe variables and conservative variables are similar in performance using the same time-step.

Keywords

Euler Equation Legendre Polynomial Haar Wavelet Eigenvalue Decomposition Conservative Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Mass Per Pettersson
    • 1
  • Gianluca Iaccarino
    • 2
  • Jan Nordström
    • 3
  1. 1.Uni ResearchBergenNorway
  2. 2.Department of Mechanical Engineering and Institute for Computational and Mathematical EngineeringStanford UniversityStanfordUSA
  3. 3.Department of Mathematics Computational MathematicsLinköping UniversityLinköpingSweden

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