References to some papers
with background information
The following list of papers gives some physical and numerical background
information on 'nsevol'. This list is in no way complete, but merely
intended to give some hints for those who want to know more.
There is also a list of
articles and student research projects that used
'nsevol'.

Abramowitz, M. and Stegun, I.A.: 1965,
Handbook of Mathematical Functions,
National Bureau of Standards, 4th printing.

Arakawa, A.: 1966,
"Computational design for longterm numerical integration of the equations
of fluid motion: twodimensional incompressible flow. Part I,"
J. Comp. Phys. 1, 119143.

Briley, W.R. and McDonald, H.: 1975,
"Solution of threedimensional compressible NavierStokes equations
by an implicit technique,"
Lecture Notes in Physics 30 (Springer, Berlin), 105110.

Hockney, R.W.: 1965,
"A fast direct solution of Poisson's equation using Fourier analysis,"
Journal of the Association for Computing Machinery 12, 95113.
*

Hockney, R.W.: 1971,
"The potential calculation and some applications,"
Methods of Computational Physics 9, 135211.
*

NAG manual, Chapter D03: Partial Differential Equations.

Nof, D.: 1990,
"Modons and monopoles on a gammaplane,"
Geophys. & Astrophys. Fluid Dynamics 52, 7187.

Orlandi, P.: 1989,
"Numerical simulation of vortices motion in presence of solid boundaries,"
in P.~Wesseling (ed.): Proceedings of the 8th GAMMConference on
numerical methods in fluid mechanics, Notes on Numerical Fluid Mechanics
(NNFM) 29, Vieweg, Braunschweig, 436445.

Orlandi, P.: 1990,
"Vortex dipole rebound from a wall,"
Phys. Fluids A 2, 14291436.

Orlandi, P.: 1993,
"Vortex dipoles impinging on circular cylinders,"
Phys. Fluids A 5, 21962206.

Orlandi, P. and Van Heijst, G.J.F.: 1992,
"Numerical simulation of tripolar vortices in 2D flow,"
Fluid Dyn. Res. 9, 179206.

Orlandi, P., Verzicco, R. and Van Heijst, G.J.F.: 1994,
"Stability of shielded vortex dipoles," in Van Heijst G.J.F. (ed.),
Modelling of Oceanic Vortices,
KNAW Colloquium Proceedings, NorthHolland, Amsterdam, pp. 169176.

Pedlosky, J.: 1987,
Geophysical Fluid Dynamics (2nd edition),
Springer Verlag, Berlin.

Press, W.H., Teukolsky, S.A., Vetterling, W.T. and
Flannery, B.P.: 1992,
Numerical Recipes in FORTRAN; The Art of Scientific Computing,
Cambridge University Press, Cambridge, 2nd ed. *

Rai, M.M. and Moin, P.: 1991,
"Direct simulations of turbulent flow using finitedifference schemes,"
J. Comp. Phys. 96, 1553.

Smith, G.D.: 1987,
Numerical Solution of Partial Differential Equations:
Finite Difference Methods,
Oxford University Press, Oxford, 3rd ed.

Van Heijst, G.J.F.: 1993,
Geophysical Fluid Dynamics  An Introduction,
postgraduate course, sept. 1993,
Eindhoven University of Technology, Eindhoven.

Van Geffen, J.H.G.M.: 1998,
Documentation of the Software Package NSEVOL,
report R1466D, Eindhoven University of Technology.

Van Heijst, G.J.F. (ed.): 1994,
Modelling of Oceanic Vortices,
KNAW Colloquium Proceedings, NorthHolland, Amsterdam.

Van Heijst, G.J.F., Feron, R., Flór, J.B. and Walsteijn, F. (eds.):
1991,
Coherent Vortex Structures in Geophysical Fluid Dynamics,
Lecture notes based on seminars given at the IMOU (R917), March 1991,
Utrecht.

Verzicco, R., Flór, J.B.,Van Heijst, G.J.F. and Orlandi, P.:
1994,
"Interaction of dipoles with cylinders: experiments and numerical
simulations," in Van Heijst G.J.F. (ed.),
Modelling of Oceanic Vortices,
KNAW Colloquium Proceedings, NorthHolland, Amsterdam, pp. 169176.

Verzicco, R., Flór, J.B.,Van Heijst, G.J.F. and Orlandi, P.:
1995,
"Numerical and experimental study of the interaction between a vortex
dipole and a circular cylinder,"
Exp. Fluids 18, 153163.

Wray, A.A.: 1987,
"Minimal storage timeadvancement schemes for spectral methods,"
unpublished manuscript.
*) These references describes the background of the Fourier Analysis
and Cyclic Reduction (FACR) method for solving the Poisson equation.
The 'modified Poisson equation', when there is bottom topography, is
solved with a NAG routine. For info on that, see
Chapter D03 Partial differential equations of the NAG manual.
<=== Vortex Evolution with a Finite Difference
Method.
<=== Numerical simulations of 2D vortex
evolution with a Finite Difference Method.
Jos van Geffen 
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created: 10 December 1996
last modified: 26 May 2001