Energy stable overset grid methods for hyperbolic problems

Nek Sharan, Carlos A Pantano-Rubino, Daniel J. Bodony

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We investigate an alternative approach of proving energy stability for hyperbolic problems on overset (or overlapping) grids. Instead of bounding the time derivative of the discrete energy in a given norm, we look at the system matrix and show stability in terms of its eigenvalues. This approach is successful for hyperbolic problems since they have a characteristic direction of propagation which yields system matrices whose eigenvalues could be estimated. The schemes are based on summation-by-parts (SBP) operators and the simultaneous approximation term (SAT) procedure for boundary conditions and interface treatments. The SAT implementation requires the knowledge of the norm matrix in which the energy estimate of the method exists. Since the complexity of determining the norm matrix prompted this investigation, we use the norm in which the single domain scheme is time stable to construct SAT treatments for overset grid and then we check its stability. The proposed treatment is energy stable for scalar hyperbolic equations irrespective of the kind and location of interpolation. The scheme is also energy stable for systems of decoupled hyperbolic equations but not for a periodic system. We show that a numerical scheme from our previous work is time stable for the periodic system.

Original languageEnglish (US)
Title of host publicationAIAA AVIATION 2014 -7th AIAA Theoretical Fluid Mechanics Conference
PublisherAmerican Institute of Aeronautics and Astronautics Inc.
ISBN (Print)9781624102936
DOIs
StatePublished - 2014
EventAIAA AVIATION 2014 -7th AIAA Theoretical Fluid Mechanics Conference 2014 - Atlanta, GA, United States
Duration: Jun 16 2014Jun 20 2014

Publication series

NameAIAA AVIATION 2014 -7th AIAA Theoretical Fluid Mechanics Conference

Other

OtherAIAA AVIATION 2014 -7th AIAA Theoretical Fluid Mechanics Conference 2014
CountryUnited States
CityAtlanta, GA
Period6/16/146/20/14

ASJC Scopus subject areas

  • Aerospace Engineering
  • Mechanical Engineering

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