# Lectures on Large-Scale Finite Difference Computation of Incompressible Fluid Flows

• Jacob E. Fromm

## Abstract

In the present section we shall attempt to describe, through example, the essentials of numerical computation of time-dependent, nonlinear fluid flows. The case in consideration will be that of incompressible flow with viscosity, described in terms of a vorticity and streamfunction. The discussions have been simplified so that the overall view of the computation procedures can be emphasized. Refinements of the individual areas, or subprograms, are presented in succeeding sections where the methods are brought up to date. Along with recommended reading the included material should permit the construction of a working program. Alternatively, the outline provided should lend itself to expansion into other areas of numerical computation of initial-boundary value problems.

## Keywords

Fluid Flow Rayleigh Number Stream Function Incompressible Fluid Mesh Point

## Preview

Unable to display preview. Download preview PDF.

## References

1. 1.
S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Oxford University Press, 1061.Google Scholar
2. 2.
R. Richtmyer, Difference Methods for Initial Value Problems, Interscience Publishers, Inc., New York, 1957.Google Scholar
3. 3.
E. Dufort and S. Frankel, Stability conditions in the numerical treatment of parabolic differential equations, Math. Tables and Other Aids to Computation 7, 135 (1953).
4. 4.
J. Fromm, A method for computing nonsteady, incompressible, viscous fluid flows, Los Alamos Scientific Laboratory Report LA 2910, Los Alamos (1963).Google Scholar
5. 5.
R. Hockney, A fast, direct solution of Poisson’s equation using Fourier analysis, Stanford Electronics Laboratory Technical Report No. 0255–1, Stanford (1964).Google Scholar
6. 6.
A. Thorn, The flow past circular cylinders at low speeds, Proc. Roy. Soc. A141, 651 (1933).Google Scholar
7. 7.
M. Kawaguti, Numerical solution of the Navier-Stokes equations for the flow around a circular cylinder at Reynolds Number 40, J. Phys. Soc. Japan 6(8), 747–757 (1953).Google Scholar
8. 8.
R. Payne, Calculations of unsteady viscous flow past a circular cylinder, J. Fluid Mech. 1(4), 81 (1958).
9. 9.
H. Sogin, Heat transfer from the rear of bluff objects to a low speed air stream, Tulane University Aeronautical Research Laboratories Report No. ARL-62–361 (1962).Google Scholar
10. 10.
F. Harlow and J. Fromm, Dynamics and heat transfer in the von Karman wake of a rectangular cylinder, Phys. Fluids 7, 1147 (1964).
11. 11.
J. Deardorff, A numerical study of two-dimensional parallel-plate convection, J. Atmos. Sci. 21, 414–438 (1964).
12. 12.
J. Fromm, Numerical solutions of the nonlinear equations for a heated fluid layer, Phys. Fluids 8, 1757 (1965).
13. 13.
H. Kuo, Solutions of the nonlinear equations of cellular convection and heat transport, J. Fluid Mech. 4(10), 611–634 (1961).

## C. Suggested Reading

1. 1.
E. I. Organick, A FORTRAN Primer, Addison-Wesley Publishing Co., Inc., Palo Alto, 1963.Google Scholar