| Title:
|
A conservative spectral element method for the approximation of compressible fluid flow (English) |
| Author:
|
Black, Kelly |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
35 |
| Issue:
|
1 |
| Year:
|
1999 |
| Pages:
|
[133]-146 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
spectral element method |
| Keyword:
|
Euler equation |
| Keyword:
|
multi-domain approach |
| MSC:
|
65M70 |
| MSC:
|
76M22 |
| MSC:
|
76M25 |
| MSC:
|
76N10 |
| idZBL:
|
Zbl 1274.76271 |
| idMR:
|
MR1705536 |
| . |
| Date available:
|
2009-09-24T19:24:01Z |
| Last updated:
|
2015-03-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135273 |
| . |
| Reference:
|
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| Reference:
|
[2] Cockburn B., Shu C. W.: TVB Runga–Kutta local projection discontinuous Galerkin finite–element method for conservation laws II: General framework.Math. Comp. 52 (1989) MR 0983311 |
| Reference:
|
[3] Cockburn B., Shu C. W.: TVB Runga–Kutta local projection discontinuous Galerkin finite–element method for conservation laws III: One dimensional systems.J. Comput. Phys. 84 (1989), 90 MR 1015355, 10.1016/0021-9991(89)90183-6 |
| Reference:
|
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| Reference:
|
[5] Courant R., Friedrichs K. O.: Supersonic Flow and Shock Waves.Applied Mathematical Sciences. Springer–Verlag, New York 1948 Zbl 0365.76001, MR 0029615 |
| Reference:
|
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| Reference:
|
[7] Harten A., Lax P. D., Leer B. Van: On upstream differencing and Godunov–type schemes for hyperbolic conservation laws.SIAM Review 25 (1983), 1, 35–61 MR 0693713, 10.1137/1025002 |
| Reference:
|
[8] Hesthaven J. S.: A stable penalty method for the compressible Navier–Stokes equations II: One dimensional domain decomposition schemes, to appea. |
| Reference:
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[9] Hesthaven J. S.: A stable penalty method for the compressible Navier–Stokes equations III: Multi dimensional domain decomposition schemes, to appea. |
| Reference:
|
[10] Hesthaven J. S., Gottlieb D.: A stable penalty method for the compressible Navier–Stokes equations.I. Open boundary conditions. SIAM J. Sci. Statist. Comput 17 (1996), 3, 579–612 Zbl 0853.76061, MR 1384253, 10.1137/S1064827594268488 |
| Reference:
|
[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 |
| Reference:
|
[12] Kopriva D. A., Kolias J. H.: A conservative staggered grid Chebychev multi–domain method for compressible flows.J. Comput. Phys. 125 (1996), 1, 244–261 MR 1381812, 10.1006/jcph.1996.0091 |
| Reference:
|
[13] Rumsey C., Leer B. van, Roe P. L.: A multidimensional flux function with applications to the Euler and Navier–Stokes equations.J. Comput. Phys. 105 (1993), 306–323 MR 1210411, 10.1006/jcph.1993.1077 |
| . |
