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On operator splitting of the Euler equations consistent with Harten's second‐order accurate TVD scheme
Author(s) -
Cooke C. H.
Publication year - 1985
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690010406
Subject(s) - total variation diminishing , mathematics , euler equations , operator splitting , operator (biology) , euler's formula , consistency (knowledge bases) , scheme (mathematics) , shock (circulatory) , order (exchange) , mathematical analysis , shock wave , geometry , physics , mechanics , medicine , biochemistry , chemistry , finance , repressor , transcription factor , economics , gene
Operator splitting is necessary in order to apply Harten's second‐order accurate, total‐variation‐diminishing (TVD) method for shock capturing to higher‐dimensional problems. Here two such splittings of the Euler equations are considered. By analytical means, one splitting is shown to be inconsistent; the other, scheme satisfies a fundamental necessary condition for consistency. Numerical results from a typical blast wave calculation employing this scheme are exhibited.