Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. (English) Zbl 1180.76043

Summary: A new technique is described for the numerical investigation of the time-dependent flow of an incompressible fluid, the boundary of which is partially confined and partially free. The full Navier-Stokes equations are written in finite-difference form, and the solution is accomplished by finite-time-step advancement. The primary dependent variables are the pressure and the velocity components. Also used is a set of marker particles which move with the fluid. The technique is called the marker and cell method. Some examples of the application of this method are presented. All nonlinear effects are completely included, and the transient aspects can be computed for as much elapsed time as desired.


76M20 Finite difference methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
76B07 Free-surface potential flows for incompressible inviscid fluids
Full Text: DOI


[1] B. Alder, S. Fernbach, and M. Rotenberg, editors,Methods in Computational Physics(Academic Press Inc., New York, 1964), Vol. 3. · Zbl 0173.52804
[2] Y. Mintz, University of California Report AFCRL 690 (1961).
[3] J. O. Wilkes, Ph.D. thesis, University of Michigan (1963).
[4] J. D. Hellums and S. W. Churchill, International Heat Transfer Conference, Boulder, Colorado (1961).
[5] J. A. Clark and H. Z. Barakat, University of Michigan, College of Engineering, Technical Report 1 (1964).
[6] Deardorff, J. Atmospheric Sci. 21 pp 419– (1964)
[7] C. E. Pearson, Sperry Rand Research Report SRRC-RR-64-17 (1964).
[8] D. Greenspan, P. C. Jain, R. Manohar, B. Noble, and A. Sakurai, University of Wisconsin, Mathematics Research Center, Technical Summary Report 482 (1964).
[9] J. E. Fromm, Los Alamos Scientific Laboratory Report LA-2910 (1963).
[10] Fromm, Phys. Fluids 6 pp 975– (1963)
[11] Harlow, Phys. Fluids 7 pp 1147– (1964)
[12] L. D. Landau and E. M. Lifshitz,Fluid Mechanics(Addison-Wesley Publishing Company, Inc., Reading, Massachusetts, 1959), p. 51.
[13] F. H. Harlow, Los Alamos Scientific Laboratory Report LAMS-2452 (1960).
[14] L. A. Santaló,Introduction to Integral Geometry(Hermann & Cie., Paris, 1953).
[15] Martin, Phil. Trans. Roy. Soc. (London) A244 pp 312– (1952)
[16] J. J. Stoker,Water Waves(Interscience Publishers, Inc., New York, 1957), Chap. 10.
[17] Whitham, Proc. Roy. Soc. (London) A227 pp 399– (1955)
[18] F. H. Harlow and J. E. Welch, (to be published).
[19] Harlow, Science 149 pp 1092– (1965)
[20] J. E. Welch, F. H. Harlow, J. P. Shannon, and B. J. Daly, Los Alamos Scientific Laboratory Report LA-3425 (1965).
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.