Cabaret finite‐difference schemes for the one‐dimensional Euler equations
In the present paper we consider second order compact upwind schemes with a space split time derivative (CABARET) applied to one‐dimensional compressible gas flows. As opposed to the conventional approach associated with incorporating adjacent space cells we use information from adjacent time layer...
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2001-12-01
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| Series: | Mathematical Modelling and Analysis |
| Subjects: | |
| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/9900 |
| _version_ | 1819227817121939456 |
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| author | V. M. Goloviznin T. P. Hynes S. A. Karabasov |
| author_facet | V. M. Goloviznin T. P. Hynes S. A. Karabasov |
| author_sort | V. M. Goloviznin |
| collection | DOAJ |
| description | In the present paper we consider second order compact upwind schemes with a space split time derivative (CABARET) applied to one‐dimensional compressible gas flows. As opposed to the conventional approach associated with incorporating adjacent space cells we use information from adjacent time layer to improve the solution accuracy. Taking the first order Roe scheme as the basis we develop a few higher (i.e. second within regions of smooth solutions) order accurate difference schemes. One of them (CABARET3) is formulated in a two‐time‐layer form, which makes it most simple and robust. Supersonic and subsonic shock‐tube tests are used to compare the new schemes with several well‐known second‐order TVD schemes. In particular, it is shown that CABARET3 is notably more accurate than the standard second‐order Roe scheme with MUSCL flux splitting.
Vienmačių Eulerio lygčių sprendimas CABARET3 baigtinių-skirtumų schemomis
Santrauka
Šiame straipsnyje nagrinejamos kompaktiškos antrosios tikslumu eiles baigtiniu skirtumu schemos, kuriose panaudota speciali išvestiniu aproksimacija. Sprendžiamas vienmatis spūdžiu duju judejimo uždavinys. Darbe pasiūlytas didesnio tikslumo schemu konstravimo metodas, kuriame išnaudojama informacija apie sprendini iš žemesnio laiko sluoksnio. CABARET3 schema yra dvisluoksne, todel jos realizavimo algoritmas yra ekonomiškas. Pateikiami skaičiavimo eksperimento rezultatai, kurie patvirtina, kad CABARET3 schema yra tikslesne už antrosios tikslumo eiles Roe schema, naudojančia MUSCL srauto išskaidyma.
First Published Online: 14 Oct 2010 |
| first_indexed | 2024-12-23T10:47:24Z |
| format | Article |
| id | doaj.art-7e73f5953228467bad8667c57dbb0525 |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-23T10:47:24Z |
| publishDate | 2001-12-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-7e73f5953228467bad8667c57dbb05252022-12-21T17:50:00ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102001-12-016210.3846/13926292.2001.9637160Cabaret finite‐difference schemes for the one‐dimensional Euler equationsV. M. Goloviznin0T. P. Hynes1S. A. Karabasov2Moscow Institute of Nuclear Safety , Russian Academy of Sciences , 52 B. Tulskaya Ulitsa, Moscow, 113191, RussiaWhittle Laboratory , Cambridge University, Engineering Department , Madingley Rd, Cambridge, CB3 ODY, UKWhittle Laboratory , Cambridge University, Engineering Department , Madingley Rd, Cambridge, CB3 ODY, UK E-mail: sak36@eng.cam.ac.uk ; Moscow Institute of Nuclear Safety , Russian Academy of Sciences , 52 B. Tulskaya Ulitsa, Moscow, 113191, RussiaIn the present paper we consider second order compact upwind schemes with a space split time derivative (CABARET) applied to one‐dimensional compressible gas flows. As opposed to the conventional approach associated with incorporating adjacent space cells we use information from adjacent time layer to improve the solution accuracy. Taking the first order Roe scheme as the basis we develop a few higher (i.e. second within regions of smooth solutions) order accurate difference schemes. One of them (CABARET3) is formulated in a two‐time‐layer form, which makes it most simple and robust. Supersonic and subsonic shock‐tube tests are used to compare the new schemes with several well‐known second‐order TVD schemes. In particular, it is shown that CABARET3 is notably more accurate than the standard second‐order Roe scheme with MUSCL flux splitting. Vienmačių Eulerio lygčių sprendimas CABARET3 baigtinių-skirtumų schemomis Santrauka Šiame straipsnyje nagrinejamos kompaktiškos antrosios tikslumu eiles baigtiniu skirtumu schemos, kuriose panaudota speciali išvestiniu aproksimacija. Sprendžiamas vienmatis spūdžiu duju judejimo uždavinys. Darbe pasiūlytas didesnio tikslumo schemu konstravimo metodas, kuriame išnaudojama informacija apie sprendini iš žemesnio laiko sluoksnio. CABARET3 schema yra dvisluoksne, todel jos realizavimo algoritmas yra ekonomiškas. Pateikiami skaičiavimo eksperimento rezultatai, kurie patvirtina, kad CABARET3 schema yra tikslesne už antrosios tikslumo eiles Roe schema, naudojančia MUSCL srauto išskaidyma. First Published Online: 14 Oct 2010https://journals.vgtu.lt/index.php/MMA/article/view/9900- |
| spellingShingle | V. M. Goloviznin T. P. Hynes S. A. Karabasov Cabaret finite‐difference schemes for the one‐dimensional Euler equations Mathematical Modelling and Analysis - |
| title | Cabaret finite‐difference schemes for the one‐dimensional Euler equations |
| title_full | Cabaret finite‐difference schemes for the one‐dimensional Euler equations |
| title_fullStr | Cabaret finite‐difference schemes for the one‐dimensional Euler equations |
| title_full_unstemmed | Cabaret finite‐difference schemes for the one‐dimensional Euler equations |
| title_short | Cabaret finite‐difference schemes for the one‐dimensional Euler equations |
| title_sort | cabaret finite difference schemes for the one dimensional euler equations |
| topic | - |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/9900 |
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