A comparison of blob methods for vortex sheet roll-up

Journal of Fluid Mechanics

Volumn 547, Issue , 2006, Pages 297-316

  Baker, Gregory R ^a   Pham, Lan D ^b  

^a OHIO STATE UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; CONVERGENCE OF NUMERICAL METHODS; CONVOLUTION; VORTEX FLOW;

BLOB METHOD; EULER EQUATIONS; VORTEX SHEET;

FLUID MECHANICS;

ASYMPTOTIC STABILITY; CONVERGENCE OF NUMERICAL METHODS; CONVOLUTION; FLUID MECHANICS; VORTEX FLOW;

VORTEX;

EID: 33644967594     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112005007305     Document Type: Article

References (23)

1. Baker, G. R. 1983 Generalized vortex methods for free-durface flows. In Waves on Fluid Interfaces (ed. R. E. Meyer). Academic.
2. Baker, G. R. & Shelley, M. J. 1990 On the connection between thin vortex layers and vortex sheets. J. Fluid Mech. 215, 161-194.
3. Beale, J. T. & Majda, A. 1985 High order accurate vortex methods with explicit velocity kernels. J. Comput. Phys. 58, 188-208.
4. Caflisch, R. E. & Orellana, O. F. 1989 Singular solutions and ill-posedness for the evolution of vortex sheets. SIAM J. Math. Anal. 20, 293-307.
5. Chorin, A. & Bernard, P. 1973 Discretization of a vortex sheet, with an example of roll-up. J. Comput. Phys. 13, 423-429.
6. Cowley, S. J., Baker, G. R. & Tanveer, S. 1999 On the formation of Moore curvature singularities in vortex sheets. J. Fluid Mech. 378, 233-268.
7. Delort J.-M. 1991 Existence de nappes de tourbillon en dimension deux. J. Am. Math. Soc. 4, 553-586.
8. Dhanak, M. R. 1994a On the equation of motion of a thin layer of uniform vorticity. Stud. Appl. Maths 92, 115-125.
9. Dhanak, M. R. 1994b Equation of motion of a diffusing vortex sheet. J. Fluid Mech. 269, 265-281.
10. Krasny, R. 1986a A study of singularity formation in a vortex sheet by the point vortex method. J. Fluid Mech. 167, 65-93.
11. Krasny, R. 1986b Desingularization of periodic vortex sheet roll-up. J. Comput. Phys. 65, 292-313.
12. Krasny, R. 1987 Computation of vortex sheet roll-up in the Trefftz plane. J. Fluid Mech. 184, 123-155.
13. Kuwahara, K. & Takami, H. 1973 Numerical studies of two-dimensional vortex motion by a system of point vortices. J. Phys. Soc. Japan 34, 247-253.
14. Liu, J.-G. & Xin, Z. 1995 Convergence of vortex methods for weak solutions to the 2D Euler equations with vortex sheet data. Commun. Pure Appl. Maths 48, 611-628.
15. Majda, A. 1993 Remarks on weak solutions for vortex sheets with a distinguished sign. Indiana Univ. Math. J. 42, 921-939.
16. Majda, A. & Bertozzi, A. 2002 Vorticity and Incompressible Flow. Cambridge University Press.
17. Moore, D. W. 1978 The equation of motion of a vortex layer of small thickness. Stud. Appl. Maths 58, 119-140.
18. Pham, L. D. 2001 Regularization of periodic vortex sheets. PhD thesis, Ohio State University.
19. Pugh, D. A. 1989 Development of vortex sheets in Boussinesg flows - formation of singularities. PhD thesis, University of London.
20. Pullin, D. I. 1981 On a generalization of Kaden's problem. J. Fluid Mech. 104, 45-53.
21. Saffman, P. G. 1992 Vortex Dynamics. Cambridge University Press.
22. Sidi, A. & Israeli, M. 1988 Quadrature methods for periodic singular and weakly singular Fredholm integral equations. J. Sci. Comput. 3, 201-219.
23. Tryggvason, G., Dahm, W. J. & Sbeih, K. 1991 Fine-structure of vortex sheet rollup by viscous and inviscid simulation. Trans. ASME I: J. Fuids Engng 113, 31-36.