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General considerations of numerical stability and accuracy in inviscid, compressible flow calculations employing primitive variables
Author(s) -
Bosman C.,
Ahrabian D.,
Kahrom M.
Publication year - 1982
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650020203
Subject(s) - inviscid flow , truncation error , stability (learning theory) , mathematics , computation , flow (mathematics) , compressible flow , truncation (statistics) , numerical stability , compressibility , numerical analysis , mathematical analysis , computer science , algorithm , geometry , mechanics , physics , statistics , machine learning
The numerical stability of a number of computation schemes currently used for three‐dimensional, inviscid, compressible flow is analysed using one‐dimensional Fourier analysis. Whereas Reference 1 analysed schemes which were modified to render them amenable to simple analysis, the present work analyses the stability of schemes as actually used by Highton, 3 Ahrabian, 1 Denton 2 and Spalding. 6 The use of current values of the variables as they become available is shown to bring a general improvement to stability margin. The manner of damping introduced by the time marching formulation is shown to be deleterious to modifications which reduce truncation error. Staggered grid schemes can be formulated to second order accuracy with better stability margin than the corresponding first order scheme. While unstaggered grid schemes can be formulated to second order error and remain stable, their stability margin becomes very small. Agreement of the theory with numerical experiments continues to be of a high order for both one and three‐dimensional disturbances.