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On the Approximate Solution of Free Boundary Problems Using Finite Differences
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Volume 17 ,  Issue 3  (July 1970) table of contents
Pages: 397 - 411  
Year of Publication: 1970
ISSN:0004-5411
Author
C. W. Cryer  University of Wisconsin, Madison, Wisconsin
Publisher
ACM  New York, NY, USA
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ABSTRACT

Two algorithms for solving free boundary problems in two dimensions are described. The algorithms use the method of finite differences and are automated versions of methods due to Southwell. The algorithms have been implemented as a general program FREEBOUN, and the numerical results that were obtained using this program are discussed.


REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

 
1
ALDER, B., FERNnACH, S., AND ROTENBERG, M. (Eds.). Methods in Computational Physics, Vol. 3: Fundamental Methods in Hydrodynamics. Academic Press, New York, 1964.
 
2
ARMS, R. J., AND GATES, L. D., JR. The computation of an axially symmetric free boundary problem on NORC, Pt. II. Rep. No. 1533, US Naval Proving Ground, Dahlgren, Va., 1957.
 
3
BERS, L., JOI~N, F., AND SCHECHTER, M. Partial Differential Equations. Interscience, Div. of Wiley, New York, 1964.
 
4
BIRKHO~F, G., AND ZARANTONEbLO, E. H. Jets, Wakes, and Cavities. Academic Press, New York, 1957.
 
5
BLOCH, E. A finite difference method for the solution of free boundary problems. Rep. No. NYO-1480-116, AEC Computing and Appl. Math. Center, Courant Inst. of Mathematical Sciences, New York U., New York, May 1969.
 
6
BRUNAVER, E.A. Axially symmetric free streamlineflow about tandem disks. M.S. thesis, Illinois Inst. of Technology, Chicago, Ill., 1951.
 
7
CtIARMONMAN, S. Coastal parallel canals with intermediate drains. J. Amer. Soc. Civil Engs, (Hydraulics Div.) 93 (1967), 13-27.
 
8
CRYER, C.W. The application of digital computers to the numerical solution of elliptic partial differential equations. Ph.D. thesis, U. of Cambridge, 1962.
 
9
---. On the approximate solution of one-phase free boundary problems in two dimensions. Tech. Rep. No. 894, Math. Res. Center, US Army, U. of Wisconsin, Madison, Wis., 1968.
 
10
DUMITRESCU, D., IONESCU, V., AND Wowtt, R. Die Anwendung des Differenzverfahrens zum Studium der Bewegung schwerer Fliissigkeiten mit freier Oberfliiche. Rev. MOch. Appl. 1 (1956), 1-81.
 
11
FORSYTHE, G. E., AND WASOW, W. R. Finite Difference Methods for Partial Differential Equations. Wiley, New York, 1960.
 
12
FRIEDRICHS, K. 0., AND KELLER, H .S . A finite difference scheme for generalized Neumann problems. In Numerical Solution of Partial Differential Equations, Bramble, J. H. (Ed.), Academic Press, New York, 1966, pp. 1-19.
 
13
GARABEDIAN, P. R. The mathematical theory of three-dimensional cavities and jets. Bull. Amer. Math. Soc. 62 (1956), 219-235.
 
14
--. Partial Differential Equations. Wiley, New York, 1964.
 
15
GILBARG, D. Jets and cavities. In Handbuch der Physik, Vol. 9: StrSmungsmechanik I I I Fluid Dynamics III}, Flfigge, S. (Ed.), Springer, Berlin, 1960, pp. 311-445.
 
16
GREENSPAN, D. On approximating extremals of functionals, Pt. I. The method and examples for boundary value problems. Bull. {nternat. Computation Center (Rome) $ (1965), 99--120.
 
17
KELLOGG, R. B., AND SPANIER, J. On optimal alternating direction parameters for singular matrices. Math. Comput. 19 (1965), 448-452.
 
18
LEWY, H. A note on harmonic functions and a hydrodynamical application. Proc. Amer. Math. Soc. 3 (1952), 111-113.
 
19
McNowN, J. S., AscE, M., Hsu, E. Y., ASCE, A. M., AND YIH, C. S, Applications of the re~ laxation technique in fluid mechanics. Trans. Amer. Soc. Civil Engs. 120 (1955), 650-699 (this paper was published earlier as Separate No. 223, Proc. Amer. Soc. Civil Engs., July 1953).
 
20
ROUSE, H., AND ABUL-FETOUH, A. Characteristics of irrotational flow through axially symmetric orifices. J. Appl. Mech. 17 (1950), 421-426.
 
21
SCHENCK, H. VAN N., JR. FORTRAN Methods in Heat Flow. Ronald Press, New York, 1963.
 
22
SOUTHWELL, R. V. Relaxation Methods in Theoretical Physics, Vol. 1. Clarendon Press, Oxford, 1946.
 
23
TAYLOR, R. L., AND BROWN, C.B. Darcy flow solutions with a free surface. J. Hydraulics Div., Proc. Amer. Soc. Civil Engs. 93 (1967), 25-33.
 
24
TREFFTZ, E. ~Tber dieKontraktion KreisfSrmige Flfissigkeitsstrahlen. Z. Math. Phys. 64 (1916), 34--61.
 
25
VARGA, R.S. Matrix Iterative Analysis. Prentice-Hall, Englewood Cliffs, N. J., 1962.
 
26
WELCH, J. E., HARLOW, F. H., SHANNON, J. P., AND DALY, B .J . The MAC method. A computing technique for solving viscous, incompressible, transient fluid-flow problems involving free surfaces. Rep. No. LA-3425, Los Alamos Scientific Lab., Los Alamos. N. M.. March 1966.
 
27
WYCKOFF, R. D., AND REED, D.W. Electric conduction model for the solution of water seepage problems. Physics 6 (1935), 395-401.
 
28
YOUNG, D. M., JR., GATES, L. D., JR., ARMS, R. J., AND ELIEZER, D.F. The computation of an axially symmetric free boundary problem on NORC. Rep. No. 1413, US Naval Proving Ground, Dahlgren, Va., 1955.