Bibliography

1
N. N. Abdelmalek, Minimum $L_\infty$ solution of underdetermined systems of linear equations, J. Approx. Theory 20, 57-69 (1977).

2
A. S. Almgren, T. Buttke, and P. Colella, A fast adaptive vortex method in three dimensions, J. Comput. Phys. 113, 177-200 (1994).

3
C. R. Anderson and M. Reider, A high order explicit method for the computation of flow about a circular cylinder, J. Comput. Phys., 125, 207-224 (1996).

4
C. R. Anderson and M. Reider, Investigation of the use of Prandtl/Navier-Stokes equation procedures for two-dimensional incompressible flows, Phys. Fluids 6, 2380-2389 (1994).

5
C. R. Anderson, An implementation of fast multipole method without multipoles, SIAM J. Sci. Stat. Comput. 13, 923-947 (1992).

6
C. R. Anderson and C. Greengard, Proceedings, AMS Seminar on Vortex dynamics and vortex methods, Seattle, Washington, 1990, Lectures in Applied Mathematics, Vol. 28, edited by C. R. Anderson and C. Greengard, (American Mathematical Society, Providence, 1991).

7
C. R. Anderson, Voriticty boundary conditions and boundary vorticity generation for two-dimensional viscous incompressible flows, J. Comput. Phys. 80, 72-97 (1989).

8
C. R. Anderson, Domain decomposition techniques and the solution of Poisson's equation in infinite domains, in Domain decomposition methods, (SIAM, Philadelphia), 129-139 (1989).

9
C. Anderson and C. Greengard, Proceedings, U.C.L.A workshop on Vortex methods, Los Angeles, California, May 20-22, 1987, Lectures Notes in Mathematics, Vol. 1360, edited by C. Anderson and C. Greengard, (Springer, New York, 1988).

10
C. R. Anderson, A method of local corrections for computing the velocity field due to a distribution of vortex blobs, J. Comput. Phys. 62, 111-123 (1986).

11
C. R. Anderson and C. Greengard, On vortex methods, SIAM J. Numer. Anal. 22, 413-440 (1986).

12
S. B. Baden and E. G. Puckett, A fast vortex method for computing 2D viscous flow, J. Comput. Phys. 91, 278-297 (1990).

13
G. Barton, Elements of Green's functions and propagation (Oxford University Press, Cambridge, 1991).

14
G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, 1987).

15
J. T. Beale and C. Greengard, Convergence of Euler-Stokes splitting of the Navier-Stokes equations, Comm. Pure Appl. Math. 47, 1083-1115 (1994).

16
J. T. Beale, G.-H. Cottet, S. Huberson, Vortex Flows and Related Numerical Methods, NATO ASI Series C, Vol. 395, edited by J. T. Beale, G.-H. Cottet, S. Huberson, (Kluwer Academic Publishers, Boston, 1993).

17
J. T. Beale and A. Majda, Higher order accurate vortex methods with explicit velocity kernels, J. Comput. Phys. 58, 188-208 (1985).

18
J. T. Beale and A. Majda, Vortex methods. II: Higher order accuracy in two and three dimensions, Math. Comput. 39, 29-52 (1982).

19
J. T. Beale and A. Majda, Rates of convergence for viscous splitting of the Navier-Stokes equations, Math. Comput. 37, 243-259 (1981).

20
M. Ben-Artzi, Global solutions of two-dimensional Navier-Stokes and Euler equations, Arch. Rational Mech. Anal. 128, 329-358 (1994).

21
D. Benfatto, R. Esposito, and M. Pulvirenti, Planar Navier-Stokes flow for singular initial data, Nonlin. Anal. Th. Meth. Appl. 9, 533-545 (1985).

22
W. Benz, Smooth particle hydrodynamics: A review, in The numerical modelling of nonlinear stellar pulsations: Problems and prospects, edited by J. R. Buchler, (Kluwer Academic Publishers, Boston, 1990), p. 269-288.

23
P. S. Bernard, A deterministic vortex sheet method for boundary layer flow, J. Comput. Phys. 117, 132-145 (1995).

24
P. S. Bernard and J. Thomas, A deterministic vortex sheet method for the three-dimensional boundary layers, in Forum on Vortex Methods for Engineering Applications, Albuquerque, New Mexico, 1995, (Sandia National Laboratory, Albuquerque, 1995), p. 85-103.

25
G. V. Bicknell, The equations of motion of particles in smoothed particle hydrodynamics, SIAM J. Stat. Comput. 12, 1198-1206 (1991).

26
H. Blasius, Grenzschichten in Flüssigkeiten mit kleiner Reibung, Z. Math. Phys. 56, 1-37 (1908).

27
E. K. Blum, A modification of the Runge-Kutta fourth-order method, Math. Comput. 16, 176-187 (1962).

28
C. Börgers and C. Peskin, A Lagrangian fractional step method for the incompressible Navier-Stokes equations on a periodic domain, J. Comput. Phys. 70, 397-438 (1987).

29
R. Bouard and M. Coutanceau, The early stage of development of the wake behind an impulsively started cylinder for $40\;<\;Re\;<\;10^4$, J. Fluid Mech. 100, 111-128 (1980).

30
J. U. Brackbill and H. M. Ruppel, FLIP: A method for adaptively zoned, particle-in-cell calculations of fluid flows in two dimensions, J. Comput. Phys. 65, 314-343 (1986).

31
H. Brezis, Remarks on the preceding paper by M. Ben-Artzi ``Global solutions of two-dimensional Navier-Stokes and Euler equations", Arch. Rational Mech. Anal. 128, 359-360 (1994).

32
J. D. Buntine and D. I. Pullin, Merger and cancellation of strained vortices, J. Fluid Mech. 205, 263-295 (1989).

33
R. E. Caflisch, Mathematical Aspects of Vortex Dynamics, SIAM Proceedings Series, edited by R. E. Caflisch, (SIAM, Philadelphia, 1989).

34
M. E. Caldaza, A combustion model for incompressible flows, Ph.D. thesis, Tulane University, 1991 (unpublished).

35
B. J. Cantwell and N. Rott, The decay of a viscous vortex pair, Phys. Fluids 31, 3213-3224 (1988).

36
J. Carrier, L. Greengard and V. Rokhlin, A fast adaptive multipole algorithm for particle simulations, SIAM J. Sci. Stat. Comput. 9, 669-686 (1988).

37
K. W. Cassel, F. T. Smith and J. D. A. Walker, The onset of instability in unsteady boundary-layer separation. J. Fluid Mech. to appear.

38
F. Cassot and S. Huberson, Numerical simulation of unsteady flows behind cylindrical structures using a finite difference-particle superposition algorithm, in Vortex flows and related numerical methods, edited by J. T. Beale, G.-H. Cottet, and S. Huberson, (Kluwer Academic Publishers, Boston, 1993), p. 159-170.

39
C.-C. Chang, C.-C. Chu, C.-C. Liu, C.-C. Chang, and S.-T. Lee, Flow induced by a pair of line vortices moving against a circular cylinder, J. Phys. Soc. Japan 64, 1557-1578 (1995).

40
C.-C. Chang and R.-L. Chern, A numerical study of flow around an impulsively started circular cylinder by a deterministic vortex method, J. Fluid Mech. 233, 243-263 (1991).

41
C.-C. Chang, Random vortex method for the Navier-Stokes equations, J. Comput. Phys. 76, 281-300 (1988).

42
A. Y. Cheer, Unsteady separated wake behind an impulsively started cylinder in slightly viscous fluid, J. Fluid Mech. 201, 485-505 (1989).

43
A. Y. Cheer, Numerical study of incompressible slightly viscous flow past blunt bodies and airfoils, SIAM J. Sci. Stat. Comput. 4, 685-705 (1983).

44
Y. Choi, J. A. C. Humphrey, and F. S. Sherman, Random-Vortex simulation of transient wall-driven flow in a rectangular enclosure, J. Comput. Phys. 75, 359-383 (1988).

45
J. P. Choquin and S. Huberson, Particles simulation of viscous flow, Comput. Fluids 17, 397-410 (1989).

46
J. P. Choquin and B. Lucquin-Desreux, Accuracy of a deterministic particle method for Navier-Stokes equations, Int. J. Numer. Methods Fluids 8, 1439-1458 (1988).

47
A. J. Chorin, Vortex Methods, PAM Report 593, Department of Mathematics University of California, Berkeley, 1993.

48
A. J. Chorin and J. E. Marsden, A Mathematical Introduction to Fluid Mechanics , (Springer-Verlag, New York, 1990).

49
A. J. Chorin, Computational Fluid Mechanics , (Academic Press, New York, 1989).

50
A. J. Chorin, Vortex models and boundary layer instability, SIAM J. Sci. Stat. Comput. 1, 1-21 (1980).

51
A. J. Chorin, Numerical methods for use in combustion modeling, in Computing methods in applied sciences and engineering, edited by R. Glowinski and J. L. Lions, (North Holland, Amsterdam, 1980), p. 229-235.

52
A. J. Chorin, Vortex sheet approximation of boundary layers, J. Comput. Phys. 27, 428-442 (1978).

53
A. J. Chorin, T. J. R. Hughes, M. F. McCracken, and J. E. Marsden, Product formulas and numerical algorithms, Comm. Pure Appl. Math. 31, 205-256 (1978).

54
A. J. Chorin, Numerical study of slightly viscous flow, J. Fluid Mech. 57, 785-796 (1973).

55
M.-H. Chou, Simulation of slightly viscous external flow by a grid-particle domain decomposition method, Computers Fluids 24, 333-347 (1995).

56
J. P. Christiansen, Numerical simulation of hydrodynamics by the method of point vortices, J. Comput. Phys. 13, 363-379 (1973).

57
K. Chua, Vortex simulation of separated flows in two and three dimensions, Ph.D. thesis, California Institute of Technology, 1990 (unpublished).

58
W. K. Chui, A numerical model of two dimensional incompressible flow and heat transfer in a boundary layer, Ph.D. thesis, Tulane University, 1993 (unpublished).

59
N. R. Clarke and O. R. Tutty, Construction and validation of a discrete vortex method for the two-dimensional incompressible Navier-Stokes equations, Computers Fluids 23, 751-783 (1994).

60
W. M. Collins and S. C. R. Dennis, The initial flow past an impulsively started circular cylinder, Quart. Journ. Mech. and Applied Math. 26, 53-75 (1973).

61
B. Couët, O. Buneman and A. Leonard, Simulation of three-dimensional incompressible flows with a Vortex-in-Cell method, J. Comput. Phys. 39, 305-328 (1981).

62
R. J. Clasen, Commun. ACM 9, 802-803 (1966).

63
R. R. Clements and D. J. Maull, The representation of sheets of vorticity by discrete vortices, Prog. Aerospace Sci. 16, 129-146 (1975).

64
G.-H. Cottet and S. Mas-Gallic, A particle method to solve the Navier-Stokes system, Numer. Math. 57, 805-827 (1990).

65
G.-H. Cottet, A particle-grid superposition method for the Navier-Stokes equations, J. Comput. Phys. 89, 301-318 (1990).

66
G.-H. Cottet Particle-grid domain decomposition methods for the Navier-Stokes equations in exterior domains, in Proceedings, AMS Seminar on Vortex dynamics and vortex methods, Seattle, Washington, 1990, Lectures in Applied Mathematics, Vol. 28, edited by C. R. Anderson and C. Greengard, (American Mathematical Society, Providence, 1991), p. 103-117.

67
G.-H. Cottet, Boundary conditions and deterministic vortex methods for the Navier-Stokes equations, in Mathematical Aspects of Vortex Dynamics, SIAM Proceedings Series, edited by R. E. Caflisch, (SIAM, Philadelphia, 1989), p. 128-143.

68
S. J. Cowley, L. L. Van Dommelen, and S. T. Lam, On the use of Lagrangian variables in unsteady boundary-layer separation, Phil. Trans. R. Soc. Lond. Series A 333, 343-378 (1990).

69
S. J. Cowley, Computer extension and analytic continuation of Blasius's expansion for impulsive flow past a circular cylinder, J. Fluid Mech. 135, 389-405 (1983).

70
M. D. Daleh, Analysis and application of the discrete vortex method, Ph.D. thesis, Princeton University, 1990 (unpublished).

71
P. Degond and F-J. Mustieles, A deterministic approximation of diffusion equations using particles, SIAM J. Sci. Stat. Comput. 11, 293-310 (1990).

72
P. Degond and S. Mas-Gallic, The weighted particle method for convection-diffusion equations Part 1: The case of an isotropic viscosity, Math. Comput. 53, 485-507 (1989).

73
T. L. Doligalski, C. R. Smith, and J. D. A. Walker, Vortex interactions with walls, Annu. Rev. Fluid. Mech. 26, 573-616 (1994).

74
C. I. Draghicescu, and M. Draghicescu, A fast algorithm for vortex blob interactions, J. Comput. Phys. 116, 69-78 (1995).

75
C. I. Draghicescu, An efficient implementation of particle methods for the incompressible Euler equations, SIAM J. Numer. Anal. 31, 1090-1108 (1994).

76
A. B. Ebiana and R. W. Bartholomew, Design considerations for the numerical filters used in vortex-in-cell algorithms, Comput. Fluids 25, 61-75 (1996).

77
J. W. Elliott, S. J. Cowley, and F. T. Smith, Breakdown of boundary layers:, i. on moving surfaces, ii. in semi-similar unsteady flow, iii. in fully unsteady flow. Geophys. Astrophys. Fluid Dynamics 25, 77-138 (1983).

78
D. Fishelov, A new vortex scheme for viscous flows J. Comput. Phys. 86, 211-224 (1990).

79
A. L. Fogelson and R. H. Dillon, Optimal smoothing in function-transport particle methods for diffusion equations, J. Comput. Phys. 109, 155-163 (1993).

80
A. L. Fogelson, Particle-method solution of two-dimensional convection-diffusion equations, J. Comput. Phys. 100, 1-16 (1992).

81
2nd International Workshop on Vortex Flows and Related Numerical Methods, Montreal, Canada, August 20-24, 1995. European Series in Applied and Industrial Mathematics, Societe de Mathematiques Appliquees et Industrielles (SMAI) of France, http://www.emath.fr/Maths/Proc/procEng.html, ISSN 1270-900X. Also to appear as CD-ROM.

82
S. I. Gass, Linear Programming (McGraw-Hill, New York, 1985).

83
A. F. Ghoniem and Y. Cagnon, Vortex simulation of laminar recirculating flow, J. Comput. Phys. 68, 346-377 (1987).

84
A. F. Ghoniem, Computational methods in turbulent reacting flow, in Proceedings, AMS/SIAM Seminar on Reacting flows: Combustion and Chemical reactors, Ithaca, New York, 1985, Lectures in Applied Mathematics, Vol. 24, edited by G. S. S. Ludford, (American Mathematical Society, Providence, 1986), p. 199-265.

85
A. F. Ghoniem and F. S. Sherman, J. Comput. Phys. 61, 1-37 (1985).

86
A. F. Ghoniem, Numerical modelling of turbulent flow in a combustion tunnel, Phil. Trans. R. Soc. Lond. A 304, 303-325 (1982).

87
Y. Giga, T. Miyakawa, and H. Osada, Two-dimensional Navier-Stokes flow with measures as initial vorticity, Arch. Rational Mech. Anal. 104, 223-250 (1988).

88
R. A. Gingold and J. J. Monaghan, Smoothed particle hydrodynamics: theory and application to non-spherical stars, Mon. Not. R. Astr. Soc. 181, 375-389 (1977).

89
V. N. Golubkin and G. B. Sizykh, Some general properties of plane-parallel viscous flows, Izv. Akad. Nauk SSSR. Mekh. Zhidk. i Gaza 3, 176-178 (1987).

90
J. Goodman, Convergence of the random vortex method, Comm. Pure Appl. Math. 40, 189-220 (1987).

91
J. Goodman, T. Y. Hou, and J. Lowengrub, Convergence of the point vortex method for the 2-D Euler equations, Comm. Pure Appl. Math. 43, 415-430 (1990).

92
J. M. R. Graham, Computation of viscous separated flow using a particle method, in Numerical Methods in Fluid Dynamics III, edited by K. W. Morton and M. J. Baines, (Clarendon press, Oxford, 1988), p. 310-317.

93
J. M. R. Graham, Application of discrete vortex methods to the computation of separated flows, in Numerical Methods in Fluid Dynamics II, edited by K. W. Morton and M. J. Baines, (Clarendon press, Oxford, 1986), p. 273-302.

94
J. M. R. Graham, The forces on sharp-edged cylinders in oscillatory flow at low Keulegan-Carpenter numbers, J. Fluid Mech. 97, 331-346 (1980).

95
M. D. Greenberg, Application of Green's functions in science and engineering (Prentice Hall, Englewood Cliffs, 1971).

96
C. Greengard, The core spreading vortex method approximates the wrong equation, J. Comput. Phys. 61, 345-348 (1985).

97
L. Greengard and V. Rokhlin, On the efficient implementation of the fast multipole algorithm, Report YALEU/DCS/RR-602, Department of Computer Science, Yale University, 1988 (unpublished).

98
P. M. Gresho, Some interesting issues in incompressible fluid dynamics, both in the continuum and in numerical simulation Adv. Appl. Mech. 28, 45-140 (1991).

99
P. M. Gresho, Incompressible fluid dynamics: some fundamental formulation issues, Annu. Rev. Fluid Mech. 23, 413-453 (1991).

100
P. M. Gresho, Some current CFD issued relevant to the incompressible Navier-Stokes equations, Comp. Method Appl. Mech. Engg. 87, 201-252 (1991).

101
P. M. Gresho and R. L. Sani, On pressure boundary conditions for the incompressible Navier-Stokes equations, Int. J. Num. Meth. Fl. 7, 1111-1145 (1987).

102
J.-L. Guermond and L. quartapelle, Equivalence of $u-p$ and $\zeta-\psi$ formulations of the time-dependent Navier-stokes equations, Int. J. Numer. Methods Fluids 18, 471-487 (1994).

103
J.-L. Guermond, S. Huberson, and W.-Z. Shen, Simulation of 2D external viscous flows by means of a domain decomposition method, J. Comput. Phys. 108, 343-352 (1993).

104
K. Gustafson and J. A. Sethian, Vortex methods and vortex motion, edited by K. Gustafson and J. A. Sethian, (SIAM, Philadelphia, 1990).

105
B. K. Hakizumwami, High Reynolds number flow past an impulsively started circular cylinder. Comput. Fluids 23, 895-902 (1994).

106
O. H. Hald, Convergence of vortex methods for Euler's equations, III, SIAM J. Num. Anal. 24, 538-582 (1987).

107
O. H. Hald, Convergence of vortex methods for Euler's equations. II, SIAM J. Num. Anal. 16, 726-755 (1979).

108
F. H. Harlow, The particle-in-cell computing method for fluid dynamics, in Fundamental Methods in Hydrodynamics, edited by B. Alder, S. Fernbach, and M. Rotenberg, (Academic Press, New York, 1964). p. 319-343.

109
T. Y. Hou, A survey of convergence analysis for point vortex methods, in Proceedings, AMS Seminar on Vortex dynamics and vortex methods, Seattle, Washington, 1990, Lectures in Applied Mathematics, Vol. 28, edited by C. R. Anderson and C. Greengard, (American Mathematical Society, Providence, 1991), p. 327-339.

110
L. N. Howard, Divergence Formulas Involving Vorticity, Arch. Rational Mech. Anal., 1, 113-123 (1957).

111
S. Huberson, A. Jollès, And W. Shen, Numerical simulation of incompressible viscous flows by means of particles method, in Proceedings, AMS Seminar on Vortex dynamics and vortex methods, Seattle, Washington, 1990, Lectures in Applied Mathematics, Vol. 28, edited by C. R. Anderson and C. Greengard, (American Mathematical Society, Providence, 1991), p. 369-384.

112
S. A. Huyer and J. R. Grant, Incorporation of boundaries for 2D triangular vorticity element methods, in Forum on Vortex Methods for Engineering Applications, Albuquerque, New Mexico, 1995, (Sandia National Laboratory, Albuquerque, 1995), p. 211-225.

113
S. A. Huyer and J. R. Grant, Computation of incipient separation via solution of the vorticty equation on a Lagrangian mesh, in 2nd International Workshop on Vortex Flows and Related Numerical Methods, Montreal, Canada, August 20-24, 1995. European Series in Applied and Industrial Mathematics, Societe de Mathematiques Appliquees et Industrielles (SMAI) of France, http://www.emath.fr/Maths/Proc/procEng.html, ISSN 1270-900X. Also to appear as CD-ROM.

114
T. Kato, The Navier-Stokes equation for an incompressible fluid in $R^2$ with a measure as the initial vorticity, Diff. Integ. Eqs. 4, 949-966 (1994).

115
T. Kato, On the classical solutions of the two-dimensional non-stationary Euler equation, Arch. Rational Mech. Anal. 25, 188-200 (1967).

116
S. N. Kempka, and J. H. Strickland, A method to simulate viscous diffusion of vorticity by convective transport of vortices at a non-solenoidal velocity, SAND93-1763, Sandia National Laboratory, 1993.

117
P. Koumoutsakos and A. Leonard, High-resolution simulations of the flow around an impulsively started cylinder using vortex methods, J. Fluid Mech. 296 , 1-38 (1995).

118
P. Koumoutsakos, A. Leonard, and F. Pépin, Boundary conditions for viscous vortex methods, J. Comput. Phys. 113, 52-61 (1994).

119
P. D. Koumoutsakos, Direct Numerical Simulations of Unsteady Separated Flows Using Vortex Methods, Ph.D. thesis, California Institute of Technology, 1993 (unpublished).

120
G. W. Kruse and P. Fischer, Center for Fluid Mechanics, Brown University, Providence, RI, (private communication), 1996.

121
K. Kuwahara and H. Takami, Numerical studies of two-dimensional vortex motion by a system of point vortices, J. Phys. Soc. Japan 34, 247-253 (1973).

122
Sir H. Lamb, Hydrodynamics (Dover, New York, 1945).

123
Y. Lecointe and J. Piquet, On the use of several compact methods for the study of unsteady incompressible viscous flow round a circular cylinder, Comput. Fluids 12, 255-280 (1984).

124
A. Leonard, Three-dimensional interactions of vortex tubes, Physica D 37, 490-496 (1989).

125
A. Leonard, Computing three-dimensional incompressible flows with vortex elements, Ann. Rev. Fluid Mech. 17, 523-559 (1985).

126
A. Leonard, Vortex methods for flow simulation, J. Comput. Phys. 37, 289-335 (1980).

127
B. P. Leonard, A stable accurate convective modelling procedure based on quadratic upstream interpolation, Comput. Methods Appl. Mech. Eng. 19, 59-98 (1979).

128
R. I. Lewis, Vortex element method for fluid dynamics analysis and engineering systems, (Cambridge University Press, Cambridge, 1990).

129
M. J. Lighthill, An informal introduction to theoretical fluid mechanics, (Clarendon Press, Oxford, 1986).

130
M. J. Lighthill, Introduction. Boundary layer theory, in Laminar boundary layers, edited by L. Rosenhead, (Dover, New York, 1988), p. 46-113.

131
C. H. Liu and L. Ting, Interaction of decaying trailing vortices in spanwise shear flow, Comput. Fluids 15, 77-92 (1987).

132
R. K. C. Lo and L. Ting, Studies of the merging of vortices, Phys. Fluids 19, 912-913 (1976).

133
T. P. Loc, Numerical analysis of unsteady secondary vortices generated by an impulsively started circular cylinder, J. Fluid Mech. 100, 111-128 (1980).

134
T. P. Loc and R. Bouard, 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 (1985).

135
D-G. Long, Convergence of the random vortex method in two dimensions, J. Amer. Math. Soc. 1, 779-804 (1988).

136
L. Lourenco, A. Krothapalli and C. Smith, Particle image velocimetry, Lecture Notes in engineering: Advances in fluid mechanics measurements, edited by M. Gad-el-Hak, (Springer-Verlag, Berlin, 1989), p. 128-199.

137
A. R. Low, Postulates of Hydrodynamics, Nature 121, 576 (1928).

138
Z. Y. Lu and T. J. Ross, Diffusing-vortex numerical scheme for solving incompressible Navier-Stokes equations, J. Comput. Phys. 95, 400-435 (1991).

139
Z. Y. Lu and S. F. Shen, Solution of unsteady viscous incompressible flow past a circular cylinder by the diffusing-vortex method, in, Numerical methods in laminar and turbulent flow, Vol. 5, Part 1, edited by C. Taylor, W. G. Habashi and M. M. Hafez, (Pineridge Press, Swansea, U.K., 1987), p. 619-631.

140
L. B. Lucy, A numerical approach to the testing of the fission hypothesis, Astr. J. 82 , 1013-1024 (1977).

141
H. J. Lugt and S. Ohring, The oblique ascent of a viscous vortex pair toward a free surface, J. Fluid Mech. 236, 461-476 (1992).

142
A. Majda and J. Sethian, The derivation and numerical solution of the equations for zero Mach number combustion, Combust. Sci. and Tech. 42, 185-205 (1985).

143
C. Marchioro and M. Pulvirenti, Mathematical theory of incompressible nonviscous fluids, Applied Mathematical Sciences, Vol. 96, (Springer-Verlag, New York, 1994).

144
C. Marchioro and M. Pulvirenti, Hydrodynamics in two dimensions and vortex theory, Comm. Math. Phys. 84, 483-503 (1982).

145
J. S. Marshall and J. R. Grant, A Lagrangian Collocation Method for Vorticity Transport in Viscous Fluid Flows, in Forum on Vortex Methods for Engineering Applications, Albuquerque, New Mexico, 1995, (Sandia National Laboratory, Albuquerque, 1995), p. 173.

146
L.-F. Martins and A. F. Ghoniem, Vortex simulations of the intake flow in a planar piston-chamber device, Int. J. Numer. Methods Fluids 12, 237-260 (1991).

147
S. Mas-Gallic and P. A. Raviart, Particle approximation of convection diffusion problems, Internal Report R86013, lab. Anal. Num., Université Pierre et Marie Curie, Paris, France, 1986 and C.R. Acad. Sci., Paris, Sér. I 305, (1987).

148
S. Mas-Gallic, Deterministic particle method: Diffusion and boundary conditions, in Proceedings, AMS Seminar on Vortex dynamics and vortex methods, Seattle, Washington, 1990, Lectures in Applied Mathematics, Vol. 28, edited by C. R. Anderson and C. Greengard, (American Mathematical Society, Providence, 1991), p. 433-465.

149
M. F. McCracken and C. S. Peskin, A vortex method for blood flow through heart valves, J. Comput. Phys. 35, 183-205 (1980).

150
F. J. McGrath, Nonstationary plane flow of viscous and ideal fluids, Arch. Rational Mech. Anal. 27, 329-348 (1968).

151
N. W. McLachlan, Bessel functions for engineers, (Clarendon Press, Oxford, 1955).

152
E. Meiburg, Lagrangian simulation of diffusion flames, Combust. Sci and Tech. 71, 1-23 (1990).

153
E. Meiburg, Incorporation and test of diffusion and strain effects in the two-dimensional vortex blob technique, J. Comput. Phys. 82, 85-93 (1989).

154
R. G. Melvin, Random choice methods for a turbulent combustion model, Ph.D. thesis, Tulane University, 1986 (unpublished).

155
F. Milinazzo and P. G. Saffman, The calculation of large Reynolds number two-dimensional flow using discrete vortices with random walk, J. Comput. Phys. 23, 380-392 (1977).

156
L. M. Milne-Thomson, Theoretical Hydrodynamics (The Macmillan Co., New York, 1955).

157
J. J. Monaghan, Smoothed particle hydrodynamics, Ann. Rev. Astron. Astrophys. 30, 543-574 (1992).

158
J. J. Monaghan, Particle methods for hydrodynamics, Computer Physics Reports 3, 71-124 (1985).

159
J. J. Monaghan, Why particle methods work ?, SIAM J. Sci. Stat. Comput. 3, 422-433 (1982).

160
F. K. Moore, On the separation of the unsteady laminar boundary layer, in Boundary Layer Research, edited by H. G. Gortler, (Springer-Verlag, Berlin, 1958), p. 296-311.

161
R. E. M. Moore and I. O. Angell, Voronoi polygons and polyhedra, J. Comput. Phys. 105, 301-305 (1993).

162
S. Nagano, M. Naita and H. Takata, A numerical analysis of the two-dimensional flow past a rectangular prism by a discrete vortex model, Comput. Fluids 10, 243-259 (1982).

163
H. N. Najm, A hybrid vortex method with deterministic diffusion, in Vortex flows and related numerical methods, edited by J. T. Beale, G.-H. Cottet, and S. Huberson, (Kluwer Academic Publishers, Boston, 1993), p. 207-222.

164
Y. Ogami and A. Y. Cheer, Simulations of unsteady compressible fluid motion by an interactive cored particle method, SIAM J. Appl. Math. 55, 1204-1226 (1995).

165
Y. Ogami and T. Akamatsu, Viscous flow simulation using the discrete vortex model-The diffusion velocity model, Comput. Fluids 19, 433-441 (1991).

166
S. Ohring and H. J. Lugt, The decay of a pair of point vortices in a viscous fluid, Phys. Fluids A 5, 3299-3301 (1993).

167
J. H. Olsen, A. Goldburg and M. Rogers, Proceedings, Symposium on aircraft wake turbulence, Seattle, Washington, September 1-3, 1970, edited by J. H. Olsen, A. Goldburg and M. Rogers, (Plenum Press, New York, 1971).

168
P. Orlandi, Vortex dipoles impinging on circular cylinders, Phys. Fluids A 5, 2196-2206 (1993).

169
R. B. Pelz and Y. Gulak, On the accuracy of diffusion particle methods, Bull. American Phys. Soc. 39, 1892 (1994).

170
F. M. Pépin, Simulation of the Flow Past an Impulsively Started Cylinder Using a Discrete Vortex Method, Ph.D. thesis, California Institute of Technology, 1990 (unpublished).

171
V. J. Peridier, F. T. Smith, and J. D. A. Walker, Vortex-induced boundary-layer separation. Part 2. Unsteady interacting boundary-layer theory, J. Fluid Mech. 232, 99-131 (1991).

172
M. Perlman, On the accuracy of vortex methods, J. Comput. Phys. 59, 200-23 (1985).

173
M.-Z. Pindera and L. Talbot, Some fluid dynamic considerations in the modeling of flames, Combust. Flame 73, 111-125 (1988).

174
H. Poincaré, Leçons sur la Théorie des Tourbillons, (Gauthier-Villars, Paris, 1893).

175
D. Potter, Computational Physics, (John Wiley, 1973).

176
L. Prandtl, Uber Flüssigkeitsbewegung bei sehr kleiner Reibung, in Ludwig Prandtl gesammelte Abhandlüngen, (Springer-Verlag, Berlin, 1961), 575-584 (1904).

177
I. Proudman and K. Johnson, Boundary-layer growth near a rear stagnation point, J. Fluid Mech. 12, 161-168 (1962).

178
E. G. Puckett, Vortex methods: An introduction and survey of selected research topics, in Incompressible computational Fluid Dynamics, edited by M. D. Gunzburger and R. A. Nicolaides, (Cambridge University Press, Cambridge, 1993), p. 335-407.

179
L. Quartapelle, Numerical solution of the incompressible Navier-Stokes equations, ISNM Vol. 113, (Birkhäuser Verlag, Boston, 1993).

180
P. A. Raviart, An Analysis of Particle methods, in Numerical Methods in Fluid Dynamics, Lecture Notes in Math., Vol. 1127, edited by F. Brezzi, (Springer-Verlag, New York/Berlin, 1985), p. 243-324.

181
M. D. Rees and K. W. Morton, Moving point, particle, and free-Lagrange methods for convection-diffusion equations SIAM J. Sci. Stat. Comput. 12, 547-572 (1991).

182
S. Roberts, Accuracy of the random vortex method for a problem with non-smooth initial conditions, J. Comput. Phys. 58, 29-43 (1985).

183
A. J. Robins and J. A. Howarth, Boundary-layer development at a two-dimensional rear stagnation point, J. Fluid Mech. 56, 161-171 (1972).

184
L. Rosenhead, The formation of vortices from a surface of discontinuity, Proc. Roy. Soc. London, Ser. A, 134, 170-192 (1932).

185
L. F. Rossi, Resurrecting core spreading vortex methods: A new scheme that is both deterministic and convergent, SIAM J. Sci. Stat. Comput. 17, 370-397 (1996).

186
L. F. Rossi, Vortex computations of wall jet flows, in Forum on Vortex Methods for Engineering Applications, Albuquerque, New Mexico, 1995, (Sandia National Laboratory, Albuquerque, 1995), p. 127-146.

187
N. Rott, Unsteady viscous flows in the vicinity of a separation point, Q. Appl. Math. 13, 444-451 (1956).

188
G. Russo, A deterministic vortex method for the Navier-Stokes equations, J. Comput. Phys. 108, 84-94 (1993).

189
P. G. Saffman, Vortex Dynamics (Cambridge University Press, Cambridge, 1995).

190
P. G. Saffman and G. R. Baker, Vortex interactions, Ann. Rev. Fluid Mech. 11, 95-122 (1979).

191
P. G. Saffman, The velocity of viscous vortex rings, Stud. Appl. Math. 49, 371-380 (1970).

192
Forum on Vortex Methods for Engineering Applications, Albuquerque, New Mexico, 1995, (Sandia National Laboratory, Albuquerque, 1995).

193
T. Sarpkaya, Vortex element methods for flow simulations, Adv. Appl. Mech. 31, 113-247 (1994).

194
T. Sarpkaya and P. Suthon, Interaction of a vortex couple with a free surface, Exp. Fluids 11, 205-217(1989).

195
T. Sarpkaya, Computational methods with vortices- The 1988 Freeman scholar lecture, J. Fluids Eng. 111, 5-52 (1989).

196
W. R. Sears, and D. P. Telionis, Boundary-layer separation in unsteady flow, SIAM J. Appl. Math. 23, 215-234, (1975).

197
W. R. Sears, Some recent developments in airfoil theory, J. Aeronaut. Sci. 23, 490-499, (1956).

198
H. Seo, Simulation of flow past a general shaped 2-D body translating and oscillating in pitch using random vortex method, Ph.D. thesis, State University of New York, Buffalo, 1991 (unpublished).

199
J. A. Sethian and A. F. Ghoniem, Validation study of vortex methods, J. Comput. Phys. 74, 283-317 (1988).

200
J. A. Sethian, Turbulent combustion in open and closed vessels, J. Comput. Phys. 54, 425-456 (1984).

201
S. Shankar and L. van Dommelen, A new diffusion procedure for vortex methods, J. Comput. Phys. 127, 88-109 (1996).

202
S. Shankar and L. L. van Dommelen, A new diffusion scheme in vortex methods for three-dimensional incompressible flows, in 2nd International Workshop on Vortex Flows and Related Numerical Methods, Montreal, Canada, August 20-24, 1995. European Series in Applied and Industrial Mathematics, Societe de Mathematiques Appliquees et Industrielles (SMAI) of France, http://www.emath.fr/Maths/Proc/procEng.html, ISSN 1270-900X. Also to appear as CD-ROM.

203
S. Shankar, S.-C. Wang, and L. L. van Dommelen, Simulating Diffusion in Vortex Methods Using a Vorticity Redistribution Technique, in Forum on Vortex Methods for Engineering Applications, Albuquerque, New Mexico, 1995, (Sandia National Laboratory, Albuquerque, 1995), p. 105-124.

204
S. Shankar and L. van Dommelen, A redistribution technique for vortex methods, Bull. Amer. Phys. Soc. 39 1922 (1995).

205
A. Sherman and M. Mascagni, A gradient random walk method for two-dimensional reaction diffusion equations, SIAM J. Comput. 15, 1280-1293 (1980).

206
W.-Z. Shen and T. P. Loc Simulation of 2D external viscous flows by means of a domain decomposition method using an influence matrix technique, Int. J. Numer. Methods Fluids 20, 1111-1136 (1995).

207
A. I. Shestakov, A hybrid vortex-ADI solution for flows of low viscosity, J. Comput. Phys. 31, 313-334 (1979).

208
D. Shiels, GALCIT, California Institute of Technology, Pasadena, CA, (private communication).

209
C. W. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing scheme, II, J. Comput. Phys. 83, 32-78 (1989).

210
G. Sod, A compressible vortex method with application to the interaction of an oblique shock wave with a boundary layer, App. Numer. Math. 8, 257-273 (1991).

211
Y. Song, Numerical simulation of flame propogations in circular cylinders, App. Numer. Math. 8, 275-288 (1991).

212
C. Shih, L. M. Lourenco, and Z. Ding, Control of unsteady separation over an impulsively started circular cylinder, in AIAA Shear flow conference, July 6-9, 1993, Orlando, FL, AIAA 93-3275, 1-12 (1993).

213
C. Shih, L. Lourenco, L. L. van Dommelen and A. Krothapalli, Unsteady flow past an airfoil pitching at a constatnt rate, AIAA J. 30, 1153-1161 (1992).

214
P. A. Smith and P. K. Stansby, An efficient surface algorithm for random-particle simulation of vorticity and heat transport, J. Comput. Phys. 81, 349-371 (1989).

215
P. A. Smith and P. K. Stansby, Impulsively started flow around a circuler cylinder by the vortex method, J. Fluid Mech. 194, 45-77 (1988).

216
P. Spalart, Numerical Simulations of Unsteady Separated Flows Using Vortex Methods, Ph.D. thesis, Stanford University, 1982 (unpublished).

217
J. Strain, 2D vortex methods and singular quadrature rules, J. Comput. Phys. 124, 131-145 (1996).

218
J. H. Strickland, S. N. Kempka, W. P. Wolfe, Viscous diffusion of vorticity in unsteady wall layers using the diffusion velocity concept, in Forum on Vortex Methods for Engineering Applications, Albuquerque, New Mexico, 1995, (Sandia National Laboratory, Albuquerque, 1995), p. 69-83.

219
J. C. Strikwerda, Finite Difference Schemes and Partial Differential Equations (Wadsworth & Brooks/Cole, Belmont, CA, 1989).

220
D. M. Summers, A random vortex simulation of Falkner-Skan boundary layer flow, J. Comput. Phys. 85, 86-103 (1989).

221
E. C. Tiemroth, The simulation of the viscous flow around a cylinder by the random vortex method, Ph.D. thesis, University of California, Berkeley, 1986 (unpublished).

222
O. Tietjens, Strömungslehre, 1st Ed., Vol. 2, (Springer-Verlag, Berlin, 1970), pp. 105-109.

223
L. Ting and R. Klein, Viscous vortical flows, Lecture notes in physics, Vol. 374, (Springer-Verlag, New York, 1991).

224
H. Trease, M. J. Fritts, and W. P. Crowley, Advances in the free-Lagrange method, edited by H. Trease, M. J. Fritts, and W. P. Crowley, (Springer-Verlag, Berlin, 1990).

225
C. Truesdell The Kinematics of Vorticity (Indiana University Press, Bloomington, 1954).

226
G. Tryggvason, J. Abdollahi-Alibek, W. W. Willmarth, and A. Hirsa, Collision of a vortex pair with a contaminated free surface, Phys. Fluids A 4, 1215-1229 (1992).

227
O. R. Tutty and N. R. Clarke, Flow past NACA aerofoils using discrete vortex method, in 2nd International Workshop on Vortex Flows and Related Numerical Methods, Montreal, Canada, August 20-24, 1995. European Series in Applied and Industrial Mathematics, Societe de Mathematiques Appliquees et Industrielles (SMAI) of France, http://www.emath.fr/Maths/Proc/procEng.html, ISSN 1270-900X. Also to appear as CD-ROM.

228
M. Vaidhyanathan, Separated flows near a free surface, Ph.D. thesis, University of California, Berkeley, 1993 (unpublished).

229
L. van Dommelen and S. Shankar, Aerodynamic forces are not affected by initial separation, submitted to Phys. Fluids.

230
L. van Dommelen and S. Shankar, Two counter-rotating diffusing vortices, Phys. Fluids A. 7, 808-819 (1995).

231
L. L. van Dommelen and S.-C. Wang, Determining unsteady 2D and 3D boundary layer separation, in Symposium on Aerodynamics & Aeroacoustics, edited by K-Y. Fung, (World Scientific Publishing, Singapore, 1994), p. 187-206.

232
L. L. van Dommelen, Lagrangian description of unsteady separation, in Proceedings, AMS Seminar on Vortex dynamics and vortex methods, Seattle, Washington, 1990, Lectures in Applied Mathematics, Vol. 28, edited by C. R. Anderson and C. Greengard, (American Mathematical Society, Providence, 1991), p. 701-718.

233
L. L. van Dommelen and E. A. Rundensteiner, Fast, adaptive summation of point forces in the two-dimensional poisson equation, J. Comput. Phys. 83, 126-147 (1989).

234
L. L. van Dommelen, Some experiments on a vortex redistribution method, American Mathematical Society regional meeting, Hoboken, NJ, Oct 21-22, (1989).

235
L. L. van Dommelen, A Vortex Redistribution Technique, FMRL Report TR-3, Department of Mechanical Engineering, Florida State University, 1989 (unpublished).

236
L. L. van Dommelen, Least-Maximum Solution Of Underdetermined Linear Systems, FMRL Report TR-4, Department of Mechanical Engineering, Florida State University, 1989 (unpublished).

237
L. L. van Dommelen, Unsteady Separation from a Lagrangian point of view, in ASME Forum on Unsteady Flow Separation, Cincinatti, Ohio, 1987, FED 52, edited by K. Ghia, p. 81-84.

238
L. L. van Dommelen, Computation of unsteady separation using Lagrangian procedures, in IUTAM Symposium on boundary layer separation, London, England, 1986., edited by F. T. Smith and S. N. Brown, (Springer-Verlag, New York, 1987), p. 73-87.

239
L. L. van Dommelen and S. F. Shen, The flow at a rear stagnation point is eventually determined by exponentially small values of the velocity, J. Fluid Mech. 157, 1-16 (1985).

240
L. L. van Dommelen Adaptive-panel vortex summation for the CYBER 205, Bull. Amer. Phys. Soc. 83 1716 (1985).

241
L. L. van Dommelen and S. F. Shen, The genesis of separation, in Proceedings, Numerical and physical aspects of aerodynamic flows, Long Beach, California, 1981, edited by T. Cebeci, (Springer-Verlag, New York, 1982), p. 293-311.

242
L. L. van Dommelen, Unsteady boundary layer separation, Ph.D. thesis, Cornell University, 1981 (unpublished).

243
L. L. van Dommelen and S. F. Shen, The spontaneous generation of the singularity in a separating laminar boundary layer, J. Comput. Phys. 38, 125-140 (1980).

244
R. Verzicco, J. B. Flor, G. J. F. Van Heijst and P. Orlandi, Numerical and experimental study of the interaction between a vortex dipole and a circular cylinder, Exp. Fluids 18, 153-163 (1995).

245
S.-C. Wang, Control of dynamic stall, Ph.D. thesis, Florida State University, 1995 (unpublished).

246
P. G. Williams, Large-time boundary-layer computations at a rear stagnation point using the asymptotic structure, Numerical and physical aspects of aerodynamic flows, edited by T. Cebeci, (Springer-Verlag, New York, 1982), p. 325-335.

247
G. S. Winckelmans and A. Leonard, Contributions to vortex particle methods for the computation of three-dimensional incompressible unsteady flows, J. Comput. Phys. 109, 247-273 (1993).

248
H. F. Winny, Rotary oscillation of a long circular cylinder in a viscous fluid, Phil. Mag. 14, 1026-1032 (1932).

249
J.-Z. Wu, X.-H. Wu, H.-Y. Ma, and J.-M. Wu, Dynamic vorticity condition: Theoretical analysis and numerical implementation, Int. J. Numer. Methods Fluids 19, 905-938 (1994).

250
H. Yamada, H. Yamabe, A. Itoh, and H. Hayashi, Numerical analysis of a flowfield produced by a pair of rectilinear vortices approaching a circular cylinder, Fluid Dyn. Res. 3, 105-110 (1988).

251
L.-A. Ying, Viscous splitting for the unbounded problem of the Navier-Stokes equations, Math. Comput. 55, 89-113 (1990).

252
X. Zhang and A. F. Ghoniem, A computational model for the rise and dispersion of wind-blown, buoyancy-driven plumes-I. Neutrally stratified atmosphere, Atmospheric Environment 27A, 2295-2311 (1993).

253
Z. C. Zheng and R. L. Ash, Study of aircraft wake vortex behaviour near the ground, AIAA. J. 34, 580-589 (1996).