A conservative spectral element method for the approximation of compressible fluid flow

Kelly Black

Kybernetika (1999)

  • Volume: 35, Issue: 1, page [133]-146
  • ISSN: 0023-5954

Abstract

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A method to approximate the Euler equations is presented. The method is a multi-domain approximation, and a variational form of the Euler equations is found by making use of the divergence theorem. The method is similar to that of the Discontinuous-Galerkin method of Cockburn and Shu, but the implementation is constructed through a spectral, multi-domain approach. The method is introduced and is shown to be a conservative scheme. A numerical example is given for the expanding flow around a point source as a comparison with the method proposed by Kopriva.

How to cite

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Black, Kelly. "A conservative spectral element method for the approximation of compressible fluid flow." Kybernetika 35.1 (1999): [133]-146. <http://eudml.org/doc/33415>.

@article{Black1999,
abstract = {A method to approximate the Euler equations is presented. The method is a multi-domain approximation, and a variational form of the Euler equations is found by making use of the divergence theorem. The method is similar to that of the Discontinuous-Galerkin method of Cockburn and Shu, but the implementation is constructed through a spectral, multi-domain approach. The method is introduced and is shown to be a conservative scheme. A numerical example is given for the expanding flow around a point source as a comparison with the method proposed by Kopriva.},
author = {Black, Kelly},
journal = {Kybernetika},
keywords = {spectral element method; Euler equation; multi-domain approach; spectral element method; Euler equation; multi-domain approach},
language = {eng},
number = {1},
pages = {[133]-146},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A conservative spectral element method for the approximation of compressible fluid flow},
url = {http://eudml.org/doc/33415},
volume = {35},
year = {1999},
}

TY - JOUR
AU - Black, Kelly
TI - A conservative spectral element method for the approximation of compressible fluid flow
JO - Kybernetika
PY - 1999
PB - Institute of Information Theory and Automation AS CR
VL - 35
IS - 1
SP - [133]
EP - 146
AB - A method to approximate the Euler equations is presented. The method is a multi-domain approximation, and a variational form of the Euler equations is found by making use of the divergence theorem. The method is similar to that of the Discontinuous-Galerkin method of Cockburn and Shu, but the implementation is constructed through a spectral, multi-domain approach. The method is introduced and is shown to be a conservative scheme. A numerical example is given for the expanding flow around a point source as a comparison with the method proposed by Kopriva.
LA - eng
KW - spectral element method; Euler equation; multi-domain approach; spectral element method; Euler equation; multi-domain approach
UR - http://eudml.org/doc/33415
ER -

References

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  4. Cockburn B., Shu C. W., TVB Runga–Kutta local projection discontinuous Galerkin finite–element method for conservation laws IV: The multidimensional case, Math. Comp. 54 (1990) (1990) MR1010597
  5. Courant R., Friedrichs K. O., Supersonic Flow and Shock Waves, Applied Mathematical Sciences. Springer–Verlag, New York 1948 Zbl0365.76001MR0029615
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  8. Hesthaven J. S., A stable penalty method for the compressible Navier–Stokes equations II: One dimensional domain decomposition schemes, to appea 
  9. Hesthaven J. S., A stable penalty method for the compressible Navier–Stokes equations III: Multi dimensional domain decomposition schemes, to appea 
  10. Hesthaven J. S., Gottlieb D., 10.1137/S1064827594268488, I. Open boundary conditions. SIAM J. Sci. Statist. Comput 17 (1996), 3, 579–612 (1996) Zbl0853.76061MR1384253DOI10.1137/S1064827594268488
  11. Kopriva D. A., A Conservative Staggered Grid Chebychev Multi–Domain Method for Compressible Flows, II: A Semi–Structured Method. NASA Contractor Report ICASE Report No. 96-15, ICASE, NASA Langley Research Center, 1996 
  12. Kopriva D. A., Kolias J. H., 10.1006/jcph.1996.0091, J. Comput. Phys. 125 (1996), 1, 244–261 (1996) MR1381812DOI10.1006/jcph.1996.0091
  13. Rumsey C., Leer B. van, Roe P. L., 10.1006/jcph.1993.1077, J. Comput. Phys. 105 (1993), 306–323 (1993) MR1210411DOI10.1006/jcph.1993.1077

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