Theoretical and numerical results of a deterministic two-dimensional vortex method

The first part of the paper reviews results obtained in earlier work: (1) The outline of the derivation of an integral equation of Fredholm type with respect to vorticity from the Navier-Stokes equations, and (2) the analytical results for two deterministic vortex methods which are based on the core...

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Bibliographic Details
Published inSadhana (Bangalore) Vol. 23; no. 5-6; pp. 419 - 441
Main Author Kida, Teruhiko
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Nature B.V 01.10.1998
Subjects
Circular cylinders
Integral equations
Mathematical models
Numerical methods
Random walk
Unsteady flow
Vortices
Vorticity
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Summary:The first part of the paper reviews results obtained in earlier work: (1) The outline of the derivation of an integral equation of Fredholm type with respect to vorticity from the Navier-Stokes equations, and (2) the analytical results for two deterministic vortex methods which are based on the corespreading model. The aim of the second part is to confirm the results of the previous analysis and to estimate the accuracy of these methods numerically. In the present paper, the model problem of a transient flow past an impulsively started circular cylinder is studied by several numerical methods. The numerical results show that (1) the Gaussian core-spreading methods are comparable with the random walk vortex method, (2) the numerical fluctuation of the deterministic methods is small, and (3) the number of panels is smaller than those in the random walk vortex method to obtain the flow with almost the same accuracy.
ISSN:0256-2499
0973-7677
DOI:10.1007/BF02744573