Open AccessCABARET FINITE‐DIFFERENCE SCHEMES FOR THE ONE‐DIMENSIONAL EULER EQUATIONS
Author(s) -
V. M. Goloviznin,
T. P. Hynes,
Sergey A. Karabasov
Publication year - 2001
Publication title -
mathematical modelling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2001.9637160
Subject(s) - euler equations , supersonic speed , mathematics , shock (circulatory) , space (punctuation) , total variation diminishing , compressibility , spacetime , finite difference , upwind scheme , compressible flow , order (exchange) , simple (philosophy) , mathematical analysis , computer science , mechanics , physics , medicine , finance , quantum mechanics , discretization , economics , operating system , philosophy , epistemology
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.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom