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Comparative criteria for finite‐difference formulations for problems of fluid flow
Author(s) -
Runchal Akshai K.
Publication year - 1977
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620111104
Subject(s) - finite difference , finite difference method , amplitude , mathematics , stability (learning theory) , flow (mathematics) , finite difference coefficient , mechanics , mathematical analysis , finite element method , geometry , computer science , physics , mixed finite element method , quantum mechanics , machine learning , thermodynamics
Abstract This paper concerns a technique for providing quantitative and qualitative answers to the questions related to accuracy and stability of finite‐difference schemes. It is applicable to both the unsteady and the steady flows. The application of the technique provides comparative information about the amplitudes and the speeds of propagation of the numerical and analytic solutions. The difference between the two solutions is characterized in terms of a ‘false’ propagation speed and ‘false’ diffusion parameters for the numerical schemes. The technique is applied to a number of commonly used finite‐difference schemes and it is concluded that the use of central differences for the convective terms and/or explicit formulations tends to increase the amplitudes and wave speeds. The opposite effects on the amplitudes and wave speeds are produced by upwind or ‘donor’ cell differences and/or implicit formulations.