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Consistency, stability and convergence of the finite‐difference equations for flow about a rotating sphere in an axial stream
Author(s) -
El Shaarawi M. A. I.,
ElBedeawi S. A.
Publication year - 1987
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.1650070804
Subject(s) - mathematics , finite difference , laminar flow , finite difference method , flow (mathematics) , mathematical analysis , convergence (economics) , partial differential equation , numerical stability , finite difference coefficient , consistency (knowledge bases) , stability (learning theory) , numerical analysis , geometry , mechanics , finite element method , physics , mixed finite element method , computer science , machine learning , economics , thermodynamics , economic growth
The finite‐difference equations which have previously been developed to solve the problem of laminar boundary layer flow about a rotating sphere in an axial stream are analysed according to the available numerical stability theories. This analysis is necessary to determine the restrictions on velocities and mesh sizes required to obtain a convergent numerical solution. Convergence can be achieved if both consistency and stability of the finite‐difference equations are fulfilled. The analysis reported in the present paper shows that the developed finite‐difference equations are consistent with their original partial differential equations. Also, the analysis proves that the developed finite‐difference procedure is numerically stable for all mesh sizes as long as the downstream meridional velocity is non‐negative, i.e.as long as no flow reversals occur within the domain of solution.