×

zbMATH — the first resource for mathematics

Theoretical and numerical results of a deterministic two-dimensional vortex method. (English) Zbl 1075.76624
MSC:
76M23 Vortex methods applied to problems in fluid mechanics
76D17 Viscous vortex flows
76D99 Incompressible viscous fluids
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Anderson C, Greengard C 1985 On vortex methods.SIAM J. Numer. Anal. 22: 413–440 · Zbl 0578.65121
[2] Beale J T, Majda A 1982 Vortex methods. I: Convergence in three dimensions; and vortex methods. II: Higher order accuracy in two and three dimensions.Math. Comput. 39: 1–27; and 29–52 · Zbl 0488.76024
[3] Bouard R, Coutanceau M 1980 The early stage of development of the wake behind an impulsively started cylinder for 40<Re<104.J. Fluid Mech. 101: 583–607
[4] Chang C-C, Chern R-L 1991 A numerical study of flow around an impulsively started circular cylinder by a deterministic vortex method.J. Fluid Mech. 233: 243–263 · Zbl 0739.76048
[5] Cheer A Y 1989 Unsteady separated wake behind an impulsively started cylinder in slightly viscous fluid.J. Fluid Mech. 201: 485–505 · Zbl 0667.76058
[6] Cheng M, Chew Y T, Luo S C 1997 A hybrid vortex method for flows over a bluff body.Int. J. Numer. Meth. Fluids 24: 253–274 · Zbl 0898.76078
[7] Chorin A J 1973 Numerical study of slightly viscous flow.J. Fluid Mech. 57: 785–796
[8] Chorin A J 1978 Vortex sheet approximation of boundary layers.J. Comput. Phys. 27: 428–442 · Zbl 0387.76040
[9] Cottet G H, Mas-Gallic S, Raviart P A 1988 Vortex methods for incompressible Euler and Navier-Stokes equations.Computational fluid dynamics and reacting gas flows (eds) B Engquist, M Luskin, A Majda (New York: Springer-Verlag) pp 47–68
[10] Degond P, Mas-Gallic S 1989 The weighted particle method for convection-diffusion equations, Part 1: The case of an isotropic viscosity.Math. Comput. 53: 485–507 · Zbl 0676.65121
[11] Goodman J 1987 Convergence of the random vortex method.Commun. Pure Appl. Math. 40: 189–220 · Zbl 0635.35077
[12] Greengard C 1985 The core-spreading vortex method approximates the wrong equation.J. Comput. Phys. 61: 345–348 · Zbl 0587.76039
[13] Ghoniem A F, Cagnon Y 1987 Vortex simulation of laminar recirculating flow.J. Comput. Phys. 68: 346–377 · Zbl 0607.76020
[14] Hakizumwami B K 1994 High Reynolds number flow past an impulsively started circular cylinder.Comput. Fluids 23: 895–902 · Zbl 0825.76505
[15] Hald O H 1987 Convergence of vortex methods for Euler’s equations, III.SIAM J. Numer. Anal. 24: 538–582 · Zbl 0616.76028
[16] Kida T, Kurita M 1996 High Reynolds number flow past an impulsively started circular cylinder (Time marching of random walk vortex method).Comput. Fluid Dynamics J. 4: 489–508
[17] Kida T, Nagata T 1993 Accuracy of the panel method with distributed sources applied to two-dimensional bluff bodies.Comput. Fluid Dynamics J. 2: 73–90
[18] Kida T, Nagata T, Nakajima T 1994 Far-field condition of vortex methods on an impulsively started two-dimensional circular cylinder with rotation.Phys. Fluids 6: 2745–2756 · Zbl 0835.76077
[19] Kida T, Nakajima T 1998Comput. Meth. Appl. Mech. Eng. (in press)
[20] Loc T P, Bouard R 1985 Numerical solution of the early stage of the unsteady viscous flow around a circular cylinder: a comparison with experimental visualization and measurements.J. Fluid Mech. 160: 93–117
[21] Long D-G 1988 Convergence of the random vortex method in two dimensions.J. Am. Math. Soc. 1: 779–804 · Zbl 0664.76024
[22] Rossi L F 1996 Resurrecting core-spreading vortex methods: A new scheme that is both deterministic and convergent.SIAM Sci. Comput. 17: 370–397 · Zbl 0848.35091
[23] Sarpkaya T 1989 Computational methods with vortices – The 1988 Freeman scholar lecture.ASME J. Fluid Eng. 115: 5–52
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.