Cabaret finite‐difference schemes for the one‐dimensional Euler equations

    V. M. Goloviznin Affiliation
    ; T. P. Hynes Affiliation
    ; S. A. Karabasov Affiliation


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


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

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How to Cite
Goloviznin, V. M., Hynes, T. P., & Karabasov, S. A. (2001). Cabaret finite‐difference schemes for the one‐dimensional Euler equations. Mathematical Modelling and Analysis, 6(2), 210-220.
Published in Issue
Dec 15, 2001
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