Efficient multi-dimensional upwinding for the steady Euler equations:
Abstract: "Multi-dimensional upwind discretizations for the steady Euler equations are studied, with the emphasis on both a good accuracy and a good efficiency. The multi-dimensional upwind methods consist of a one-dimensional Riemann solver with a locally rotated left and right cell face state...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
1991
|
| Schriftenreihe: | Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM
1991,7 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "Multi-dimensional upwind discretizations for the steady Euler equations are studied, with the emphasis on both a good accuracy and a good efficiency. The multi-dimensional upwind methods consist of a one-dimensional Riemann solver with a locally rotated left and right cell face state, the rotation angle depending on the local flow solution. On the basis of a model equation, we make first a study of the accuracy and stability properties of some of these multi-dimensional upwind schemes. One novel multi-dimensional scheme is derived for which smoothing analysis of point Gauss-Seidel relaxation shows that despite its rather low numerical diffusion, it still enables a good acceleration by multigrid Another novel multi-dimensional scheme is derived which has no numerical diffusion in crosswind direction, and of which convergence analysis shows that its corresponding discretized equations can be solved efficiently by means of defect correction iteration with in the inner multigrid iteration the former multi-dimensional scheme. It is shown that for Euler flows, an appropriate local rotation angle can be found by maximizing a Riemann invariant along the middle subpath of the wave path in state space. For the steady, two-dimensional Euler equations, numerical results are presented for some supersonic test cases with an oblique contact discontinuity and for some supersonic test cases with an oblique shock wave The numerical results are in good agreement with the theoretical predictions. Comparisons are made with results obtained by standard one- dimensional upwind schemes. The multi-dimensional results obtained compare very well, both with respect to accuracy and efficiency. |
| Beschreibung: | 35 S. |
Internformat
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| 100 | 1 | |a Hemker, Pieter W. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Efficient multi-dimensional upwinding for the steady Euler equations |c P. W. Hemker ; B. Koren |
| 264 | 1 | |a Amsterdam |c 1991 | |
| 300 | |a 35 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM |v 1991,7 | |
| 520 | 3 | |a Abstract: "Multi-dimensional upwind discretizations for the steady Euler equations are studied, with the emphasis on both a good accuracy and a good efficiency. The multi-dimensional upwind methods consist of a one-dimensional Riemann solver with a locally rotated left and right cell face state, the rotation angle depending on the local flow solution. On the basis of a model equation, we make first a study of the accuracy and stability properties of some of these multi-dimensional upwind schemes. One novel multi-dimensional scheme is derived for which smoothing analysis of point Gauss-Seidel relaxation shows that despite its rather low numerical diffusion, it still enables a good acceleration by multigrid | |
| 520 | 3 | |a Another novel multi-dimensional scheme is derived which has no numerical diffusion in crosswind direction, and of which convergence analysis shows that its corresponding discretized equations can be solved efficiently by means of defect correction iteration with in the inner multigrid iteration the former multi-dimensional scheme. It is shown that for Euler flows, an appropriate local rotation angle can be found by maximizing a Riemann invariant along the middle subpath of the wave path in state space. For the steady, two-dimensional Euler equations, numerical results are presented for some supersonic test cases with an oblique contact discontinuity and for some supersonic test cases with an oblique shock wave | |
| 520 | 3 | |a The numerical results are in good agreement with the theoretical predictions. Comparisons are made with results obtained by standard one- dimensional upwind schemes. The multi-dimensional results obtained compare very well, both with respect to accuracy and efficiency. | |
| 650 | 4 | |a Defect correction methods (Numerical analysis) | |
| 650 | 4 | |a Euler's numbers | |
| 650 | 4 | |a Multigrid methods (Numerical analysis) | |
| 700 | 1 | |a Koren, Barry |e Verfasser |4 aut | |
| 810 | 2 | |a Afdeling Numerieke Wiskunde: Report NM |t Centrum voor Wiskunde en Informatica <Amsterdam> |v 1991,7 |w (DE-604)BV010177152 |9 1991,7 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006764840 | ||
Datensatz im Suchindex
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| author | Hemker, Pieter W. Koren, Barry |
| author_facet | Hemker, Pieter W. Koren, Barry |
| author_role | aut aut |
| author_sort | Hemker, Pieter W. |
| author_variant | p w h pw pwh b k bk |
| building | Verbundindex |
| bvnumber | BV010183075 |
| ctrlnum | (OCoLC)24807112 (DE-599)BVBBV010183075 |
| format | Book |
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| id | DE-604.BV010183075 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:47:58Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006764840 |
| oclc_num | 24807112 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM |
| owner_facet | DE-91G DE-BY-TUM |
| physical | 35 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| record_format | marc |
| series2 | Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM |
| spelling | Hemker, Pieter W. Verfasser aut Efficient multi-dimensional upwinding for the steady Euler equations P. W. Hemker ; B. Koren Amsterdam 1991 35 S. txt rdacontent n rdamedia nc rdacarrier Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM 1991,7 Abstract: "Multi-dimensional upwind discretizations for the steady Euler equations are studied, with the emphasis on both a good accuracy and a good efficiency. The multi-dimensional upwind methods consist of a one-dimensional Riemann solver with a locally rotated left and right cell face state, the rotation angle depending on the local flow solution. On the basis of a model equation, we make first a study of the accuracy and stability properties of some of these multi-dimensional upwind schemes. One novel multi-dimensional scheme is derived for which smoothing analysis of point Gauss-Seidel relaxation shows that despite its rather low numerical diffusion, it still enables a good acceleration by multigrid Another novel multi-dimensional scheme is derived which has no numerical diffusion in crosswind direction, and of which convergence analysis shows that its corresponding discretized equations can be solved efficiently by means of defect correction iteration with in the inner multigrid iteration the former multi-dimensional scheme. It is shown that for Euler flows, an appropriate local rotation angle can be found by maximizing a Riemann invariant along the middle subpath of the wave path in state space. For the steady, two-dimensional Euler equations, numerical results are presented for some supersonic test cases with an oblique contact discontinuity and for some supersonic test cases with an oblique shock wave The numerical results are in good agreement with the theoretical predictions. Comparisons are made with results obtained by standard one- dimensional upwind schemes. The multi-dimensional results obtained compare very well, both with respect to accuracy and efficiency. Defect correction methods (Numerical analysis) Euler's numbers Multigrid methods (Numerical analysis) Koren, Barry Verfasser aut Afdeling Numerieke Wiskunde: Report NM Centrum voor Wiskunde en Informatica <Amsterdam> 1991,7 (DE-604)BV010177152 1991,7 |
| spellingShingle | Hemker, Pieter W. Koren, Barry Efficient multi-dimensional upwinding for the steady Euler equations Defect correction methods (Numerical analysis) Euler's numbers Multigrid methods (Numerical analysis) |
| title | Efficient multi-dimensional upwinding for the steady Euler equations |
| title_auth | Efficient multi-dimensional upwinding for the steady Euler equations |
| title_exact_search | Efficient multi-dimensional upwinding for the steady Euler equations |
| title_full | Efficient multi-dimensional upwinding for the steady Euler equations P. W. Hemker ; B. Koren |
| title_fullStr | Efficient multi-dimensional upwinding for the steady Euler equations P. W. Hemker ; B. Koren |
| title_full_unstemmed | Efficient multi-dimensional upwinding for the steady Euler equations P. W. Hemker ; B. Koren |
| title_short | Efficient multi-dimensional upwinding for the steady Euler equations |
| title_sort | efficient multi dimensional upwinding for the steady euler equations |
| topic | Defect correction methods (Numerical analysis) Euler's numbers Multigrid methods (Numerical analysis) |
| topic_facet | Defect correction methods (Numerical analysis) Euler's numbers Multigrid methods (Numerical analysis) |
| volume_link | (DE-604)BV010177152 |
| work_keys_str_mv | AT hemkerpieterw efficientmultidimensionalupwindingforthesteadyeulerequations AT korenbarry efficientmultidimensionalupwindingforthesteadyeulerequations |