Analysis of the convergence of iterative implicit and defect-correction algorithms for hyperbolic problems:
Abstract: "This paper studies the convergence of unfactored implicit schemes for the solution of the steady discrete Euler equations. In these schemes first and second order accurate discretisations are simultaneously used. The close resemblance of these schemes with iterative defect correction...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
1990
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| Schriftenreihe: | Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM
1990,4 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "This paper studies the convergence of unfactored implicit schemes for the solution of the steady discrete Euler equations. In these schemes first and second order accurate discretisations are simultaneously used. The close resemblance of these schemes with iterative defect correction is shown. Linear model problems are introduced for the one-dimensional and the two-dimensional cases. These model problems are analyzed in detail both by Fourier and by matrix analyses. The convergence behaviour appears to be strongly dependent on a parameter [beta] that determines the amount of upwinding in the discretisation of the second order scheme In general, in the iteration, after an impulsive initial phase a slower psuedo-convective (or Fourier) phase can be distinguished, and finally again a faster asymptotic phase. The extreme parameter values [beta] = 0 (no upwinding) and [beta] = 1 (full second order upwinding) both appear as special cases for which the convergence behaviour degenerates. They are not recommended for practical use. For the intermediate values of [beta] the pseudo-convection phase is less significant. Fromm's scheme ([beta]=1/2) or van Leer's third order scheme ([beta]=1/3) show a quite satisfactory convergence behaviour. In this paper, first the linear convection problem in one and two dimensions is studied in detail Differences between the various cases are signalized. In the last section experiments are shown for the Euler equations, including comments on how the theory is well or partially verified depending on the problem. |
| Beschreibung: | 82 S. |
Internformat
MARC
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| 041 | 0 | |a eng | |
| 049 | |a DE-91G | ||
| 100 | 1 | |a Désidéri, Jean-Antoine |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Analysis of the convergence of iterative implicit and defect-correction algorithms for hyperbolic problems |c J.-A. Desideri ; P. W. Hemker |
| 264 | 1 | |a Amsterdam |c 1990 | |
| 300 | |a 82 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 1990,4 | |
| 520 | 3 | |a Abstract: "This paper studies the convergence of unfactored implicit schemes for the solution of the steady discrete Euler equations. In these schemes first and second order accurate discretisations are simultaneously used. The close resemblance of these schemes with iterative defect correction is shown. Linear model problems are introduced for the one-dimensional and the two-dimensional cases. These model problems are analyzed in detail both by Fourier and by matrix analyses. The convergence behaviour appears to be strongly dependent on a parameter [beta] that determines the amount of upwinding in the discretisation of the second order scheme | |
| 520 | 3 | |a In general, in the iteration, after an impulsive initial phase a slower psuedo-convective (or Fourier) phase can be distinguished, and finally again a faster asymptotic phase. The extreme parameter values [beta] = 0 (no upwinding) and [beta] = 1 (full second order upwinding) both appear as special cases for which the convergence behaviour degenerates. They are not recommended for practical use. For the intermediate values of [beta] the pseudo-convection phase is less significant. Fromm's scheme ([beta]=1/2) or van Leer's third order scheme ([beta]=1/3) show a quite satisfactory convergence behaviour. In this paper, first the linear convection problem in one and two dimensions is studied in detail | |
| 520 | 3 | |a Differences between the various cases are signalized. In the last section experiments are shown for the Euler equations, including comments on how the theory is well or partially verified depending on the problem. | |
| 650 | 4 | |a Lagrange equations | |
| 700 | 1 | |a Hemker, Pieter W. |e Verfasser |4 aut | |
| 810 | 2 | |a Afdeling Numerieke Wiskunde: Report NM |t Centrum voor Wiskunde en Informatica <Amsterdam> |v 1990,4 |w (DE-604)BV010177152 |9 1990,4 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006767883 | ||
Datensatz im Suchindex
| _version_ | 1804124588249972736 |
|---|---|
| any_adam_object | |
| author | Désidéri, Jean-Antoine Hemker, Pieter W. |
| author_facet | Désidéri, Jean-Antoine Hemker, Pieter W. |
| author_role | aut aut |
| author_sort | Désidéri, Jean-Antoine |
| author_variant | j a d jad p w h pw pwh |
| building | Verbundindex |
| bvnumber | BV010187232 |
| ctrlnum | (OCoLC)23456858 (DE-599)BVBBV010187232 |
| format | Book |
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| id | DE-604.BV010187232 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:48:03Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006767883 |
| oclc_num | 23456858 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM |
| owner_facet | DE-91G DE-BY-TUM |
| physical | 82 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| record_format | marc |
| series2 | Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM |
| spelling | Désidéri, Jean-Antoine Verfasser aut Analysis of the convergence of iterative implicit and defect-correction algorithms for hyperbolic problems J.-A. Desideri ; P. W. Hemker Amsterdam 1990 82 S. txt rdacontent n rdamedia nc rdacarrier Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM 1990,4 Abstract: "This paper studies the convergence of unfactored implicit schemes for the solution of the steady discrete Euler equations. In these schemes first and second order accurate discretisations are simultaneously used. The close resemblance of these schemes with iterative defect correction is shown. Linear model problems are introduced for the one-dimensional and the two-dimensional cases. These model problems are analyzed in detail both by Fourier and by matrix analyses. The convergence behaviour appears to be strongly dependent on a parameter [beta] that determines the amount of upwinding in the discretisation of the second order scheme In general, in the iteration, after an impulsive initial phase a slower psuedo-convective (or Fourier) phase can be distinguished, and finally again a faster asymptotic phase. The extreme parameter values [beta] = 0 (no upwinding) and [beta] = 1 (full second order upwinding) both appear as special cases for which the convergence behaviour degenerates. They are not recommended for practical use. For the intermediate values of [beta] the pseudo-convection phase is less significant. Fromm's scheme ([beta]=1/2) or van Leer's third order scheme ([beta]=1/3) show a quite satisfactory convergence behaviour. In this paper, first the linear convection problem in one and two dimensions is studied in detail Differences between the various cases are signalized. In the last section experiments are shown for the Euler equations, including comments on how the theory is well or partially verified depending on the problem. Lagrange equations Hemker, Pieter W. Verfasser aut Afdeling Numerieke Wiskunde: Report NM Centrum voor Wiskunde en Informatica <Amsterdam> 1990,4 (DE-604)BV010177152 1990,4 |
| spellingShingle | Désidéri, Jean-Antoine Hemker, Pieter W. Analysis of the convergence of iterative implicit and defect-correction algorithms for hyperbolic problems Lagrange equations |
| title | Analysis of the convergence of iterative implicit and defect-correction algorithms for hyperbolic problems |
| title_auth | Analysis of the convergence of iterative implicit and defect-correction algorithms for hyperbolic problems |
| title_exact_search | Analysis of the convergence of iterative implicit and defect-correction algorithms for hyperbolic problems |
| title_full | Analysis of the convergence of iterative implicit and defect-correction algorithms for hyperbolic problems J.-A. Desideri ; P. W. Hemker |
| title_fullStr | Analysis of the convergence of iterative implicit and defect-correction algorithms for hyperbolic problems J.-A. Desideri ; P. W. Hemker |
| title_full_unstemmed | Analysis of the convergence of iterative implicit and defect-correction algorithms for hyperbolic problems J.-A. Desideri ; P. W. Hemker |
| title_short | Analysis of the convergence of iterative implicit and defect-correction algorithms for hyperbolic problems |
| title_sort | analysis of the convergence of iterative implicit and defect correction algorithms for hyperbolic problems |
| topic | Lagrange equations |
| topic_facet | Lagrange equations |
| volume_link | (DE-604)BV010177152 |
| work_keys_str_mv | AT desiderijeanantoine analysisoftheconvergenceofiterativeimplicitanddefectcorrectionalgorithmsforhyperbolicproblems AT hemkerpieterw analysisoftheconvergenceofiterativeimplicitanddefectcorrectionalgorithmsforhyperbolicproblems |