On the numerical solution of the regularized Birkhoff equations
Author:
Christoph Börgers
Journal:
Math. Comp. 53 (1989), 141156
MSC:
Primary 76C05; Secondary 7608, 76D25
MathSciNet review:
969481
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Abstract 
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Abstract: The Birkhoff equations for the evolution of vortex sheets are regularized in a way proposed by Krasny. The convergence of numerical approximations to a fixed regularization is studied theoretically and numerically. The numerical test problem is a twodimensional inviscid jet.
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 G. Birkhoff, Helmholtz and Taylor Instability, Proc. Sympos. Appl. Math., vol. 13, Amer. Math. Soc., Providence, R. I., 1962, pp. 5576. MR 0137423 (25:875)
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 D. R. Boldman & P. F. Brinich & M. E. Goldstein, "Vortex shedding from a blunt trailing edge with equal and unequal external mean velocities," J. Fluid Mech., v. 75, 1976, pp. 721735.
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 [7]
 A. J. Chorin, "Numerical study of slightly viscous flow," J. Fluid Mech., v. 57, 1973, pp. 785796. MR 0395483 (52:16280)
 [8]
 C. W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations, PrenticeHall, Englewood Cliffs, N. J., 1971. MR 0315898 (47:4447)
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 R. Krasny, "A study of singularity formation in a vortex sheet by the pointvortex approximation," J. Fluid Mech., v. 167, 1986, pp. 6593. MR 851670 (87g:76028)
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 R. Krasny, "Desingularization of periodic vortex sheet rollup," J. Comput. Phys., v. 65, 1986, pp. 292313.
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 R. Krasny, "Computation of vortex sheet rollup in the Trefftz plane," J. Fluid Mech., v. 184, 1987, pp. 123155. MR 979557
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 E. Meiburg, "On the role of subharmonic perturbations in the far wake," J. Fluid Mech., v. 177, 1987, pp. 83107.
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 D. W. Moore, "The spontaneous appearance of a singularity in the shape of an evolving vortex sheet," Proc. Roy. Soc. London Ser. A, v. 365, 1979, pp. 105119. MR 527594 (80b:76006)
 [14]
 C. Sulem, P. L. Sulem, C. Bardos & U. Frisch, "Finite time analyticity for the two and threedimensional KelvinHelmholtz instability," Comm. Math. Phys., v. 80, 1981, pp. 485516. MR 628507 (83d:76012)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198909694812
PII:
S 00255718(1989)09694812
Article copyright:
© Copyright 1989 American Mathematical Society
