Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



On the numerical solution of the regularized Birkhoff equations

Author: Christoph Börgers
Journal: Math. Comp. 53 (1989), 141-156
MSC: Primary 76C05; Secondary 76-08, 76D25
MathSciNet review: 969481
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 two-dimensional inviscid jet.

References [Enhancements On Off] (What's this?)

  • [1] F. H. Abernathy & R. E. Kronauer, "The formation of vortex streets," J. Fluid Mech., v. 13, 1962, pp. 1-20. MR 0138296 (25:1743)
  • [2] H. Aref & E. D. Siggia, "Evolution and breakdown of a vortex street in two dimensions," J. Fluid Mech., v. 109, 1981, pp. 435-463.
  • [3] G. Birkhoff, Helmholtz and Taylor Instability, Proc. Sympos. Appl. Math., vol. 13, Amer. Math. Soc., Providence, R. I., 1962, pp. 55-76. MR 0137423 (25:875)
  • [4] 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. 721-735.
  • [5] R. Caflisch & J. Lowengrub, Convergence of the Vortex Method for Vortex Sheets, Preprint, 1988. MR 1014874 (91g:76073)
  • [6] R. Caflisch & O. Orellana, "Long-time existence for a slightly perturbed vortex sheet," Comm. Pure Appl. Math., v. 39, 1986, pp. 807-838. MR 859274 (87m:76018)
  • [7] A. J. Chorin, "Numerical study of slightly viscous flow," J. Fluid Mech., v. 57, 1973, pp. 785-796. MR 0395483 (52:16280)
  • [8] C. W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, N. J., 1971. MR 0315898 (47:4447)
  • [9] R. Krasny, "A study of singularity formation in a vortex sheet by the point-vortex approximation," J. Fluid Mech., v. 167, 1986, pp. 65-93. MR 851670 (87g:76028)
  • [10] R. Krasny, "Desingularization of periodic vortex sheet roll-up," J. Comput. Phys., v. 65, 1986, pp. 292-313.
  • [11] R. Krasny, "Computation of vortex sheet roll-up in the Trefftz plane," J. Fluid Mech., v. 184, 1987, pp. 123-155. MR 979557
  • [12] E. Meiburg, "On the role of subharmonic perturbations in the far wake," J. Fluid Mech., v. 177, 1987, pp. 83-107.
  • [13] 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. 105-119. MR 527594 (80b:76006)
  • [14] C. Sulem, P. L. Sulem, C. Bardos & U. Frisch, "Finite time analyticity for the two- and three-dimensional Kelvin-Helmholtz instability," Comm. Math. Phys., v. 80, 1981, pp. 485-516. MR 628507 (83d:76012)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 76C05, 76-08, 76D25

Retrieve articles in all journals with MSC: 76C05, 76-08, 76D25

Additional Information

Article copyright: © Copyright 1989 American Mathematical Society

American Mathematical Society