| Title:
|
A numerical method for unsteady flows (English) |
| Author:
|
Botta, Nicola |
| Author:
|
Jeltsch, Rolf |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
40 |
| Issue:
|
3 |
| Year:
|
1995 |
| Pages:
|
175-201 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A high resolution finite volume method for the computation of unsteady solutions of the Euler equations in two space dimensions is presented and validated. The scheme is of Godunov-type. The first order part of the flux function uses the approximate Riemann problem solver of Pandolfi and here a new derivation of this solver is presented. This construction paves the way to understand the conditions under which the scheme satisfies an entropy condition. The extension to higher order is done by applying ideas of LeVeque to the approximate Riemann problem solution. A detailed validation of the scheme is done on one and two dimensional test problems. (English) |
| Keyword:
|
finite volume method |
| Keyword:
|
Euler equations |
| Keyword:
|
Riemann problem |
| MSC:
|
05M25 |
| MSC:
|
65M05 |
| MSC:
|
76H05 |
| MSC:
|
76M25 |
| idZBL:
|
Zbl 0831.76064 |
| idMR:
|
MR1332313 |
| DOI:
|
10.21136/AM.1995.134290 |
| . |
| Date available:
|
2009-09-22T17:47:48Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134290 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[9] R.J. LeVeque: Hyperbolic conservation laws and numerical methods.Technical Report No. 90-3, University of Washington, 1990. |
| Reference:
|
[10] R.J. LeVeque: Simplified multi-dimensional flux limiter methods.. Zbl 0801.76069 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[15] M. Pandolfi: A contribution to the numerical prediction of unsteady flows.AIAA Journ. 22 (1984), no. 5, 602. Zbl 0542.76090, 10.2514/3.48491 |
| Reference:
|
[16] P.L. Roe: Some contributions to the modeling of discontinuous flows.Lecture Notes in Appl. Math. 22 (1985), 163–193. MR 0818787 |
| Reference:
|
[17] C.W. Schulz-Rinne: The Riemann problem for two-dimensional gas dynamics and new limiters for high-order schemes.PhD thesis, Swiss Federal Institute of Technology, Diss. ETH No. 10297, 1993. MR 1262404 |
| Reference:
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[18] G. Strang: On the construction and comparison of difference schemes.SIAM J. Numer. Anal. 5 (1968), 506–517. MR 0235754, 10.1137/0705041 |
| Reference:
|
[19] P.R. Woodward and P. Colella: The numerical simulation of two dimensional fluid flow with strong shocks.J. Comput. Phys. 54 (1984), 115–173. MR 0748569, 10.1016/0021-9991(84)90142-6 |
| . |
