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Numerical study of slightly viscous flow

Published online by Cambridge University Press:  29 March 2006

Alexandre Joel Chorin
Alexandre Joel Chorin
Affiliation:
Department of Mathematics, University of California, Berkeley
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Abstract

A numerical method for solving the time-dependent Navier–Stokes equations in two space dimensions at high Reynolds number is presented. The crux of the method lies in the numerical simulation of the process of vorticity generation and dispersal, using computer-generated pseudo-random numbers. An application to flow past a circular cylinder is presented.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 57 , Issue 4 , 6 March 1973 , pp. 785 - 796
Copyright
© 1973 Cambridge University Press

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References

Batchelor, G. K. 1960 The Theory of Homogeneous Turbulence. Cambridge University Press.
Batchelor, G. K. 1967 Am Introduction to Fluid Mechanics. Cambridge University Press.
Chorin, A. J. 1969a On the convergence of discrete approximations to the Navier-Stokes equations. Math. Comp. 23, 341.Google Scholar
Chorin, A. J. 1969b Inertial range flow and turbulence cascades. A.E.C. R. & D. Rep. NYO-1480-135.Google Scholar
Chorin, A. J. 1970 Computational aspects of the turbulence problem. In Proc. 2nd Int. Conf. on Numerical Methods in Fluid Mech., p. 285. Springer.
Chorin, A. J. 1972 A vortex method for the study of rapid flow. In Proc. 3rd Int. Conf. on Numerical Methods in Fluid Mech. Springer.
Chorin, A. J. 1973 Representations of random flow. (To appear.)
Dushane, T. E. 1973 Convergence of a vortex method for Euler's equations. (To appear.)
Einstein, A. 1956 Investigation on the Theory of Brownian Motion. Dover.
Glimm, J. 1965 Solutions in the large for nonlinear hyperbolic systems of conservation laws. Comm. Pure Appl. Math. 18, 697.Google Scholar
Keller, H.B. & Takami, H. 1966 Numerical studies of steady viscous flow about cylinders. In Numerical Solutions of Nonlinear Differential Equations (ed. D. Green-span), p. 115. Wiley.
Kellogg, O. D. 1929 Foundations of Potential Theory. New York: Ungar. (Also available through Dover Publications.)
Paley, R. E. A. C. & Wiener, N. 1934 Fourier Transforms in the Complex Domain, Colloquium Publications, vol. 19. Providence : Am. Math. Soc.
Schlichtinc, H. 1960 Boundary Layer Theory. McGraw-Hill.
Smith, A. M. O. 1970 Recent progress in the calculation of potential flows. Proc. 7th Symp. Naval Hydrodynamics. Office of Naval Research.
Wax, N. 1954 Selected Papers on Noise and Stochastic Processes. Dover.