Numerical solution of the NavierStokes equations
Author:
Alexandre Joel Chorin
Journal:
Math. Comp. 22 (1968), 745762
MSC:
Primary 65.68
MathSciNet review:
0242392
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Abstract: A finitedifference method for solving the timedependent NavierStokes equations for an incompressible fluid is introduced. This method uses the primitive variables, i.e. the velocities and the pressure, and is equally applicable to problems in two and three space dimensions. Test problems are solved, and an application to a threedimensional convection problem is presented.
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A. J. Chorin, "A numerical method for solving incompressible viscous flow problems," J. Computational Physics, v. 2, 1967, p. 12.
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J. O. Wilkes, "The finite difference computation of natural convection in an enclosed cavity," Ph.D. Thesis, Univ. of Michigan, Ann Arbor, Mich., 1963.
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(Russian). MR
0183127 (32 #609)
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Englewood Cliffs, N.J., 1962. MR 0158502
(28 #1725)
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R. Garabedian, Estimation of the relaxation factor
for small mesh size, Math. Tables Aids
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(19,583a), http://dx.doi.org/10.1090/S00255718195600888027
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C. E. Pearson, "A computational method for time dependent two dimensional incompressible viscous flow problems," Report No. SRRCRR6417, Sperry Rand Research Center, Sudbury, Mass., 1964.
 [8]
Alexandre
Joel Chorin, The numerical solution of the
NavierStokes equations for an incompressible fluid, Bull. Amer. Math. Soc. 73 (1967), 928–931. MR 0216814
(35 #7643), http://dx.doi.org/10.1090/S000299041967118536
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0128226 (23 #B1270)
 [10]
A. J. Chorin, "Numerical study of thermal convection in a fluid layer heated from below," AEC Research and Development Report No. NYO148061, New York Univ., Aug. 1966.
 [11]
P. H. Rabinowitz, "Nonuniqueness of rectangular solutions of the Benard problem," Arch. Rational Mech. Anal. (To appear.)
 [12]
E. L. Koschmieder, "On convection on a uniformly heated plane," Beitr. Physik. Alm., v. 39, 1966, p. 1.
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H. T. Rossby, "Experimental study of Benard convection with and without rotation," Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, Mass., 1966.
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F. Busse, "On the stability of two dimensional convection in a layer heated from below," J. Math. Phys., v. 46, 1967, p. 140.
 [1]
 H. Fujita & T. Kato, "On the NavierStokes initial value problem. I," Arch. Rational Mech. Anal., v. 16, 1964, pp. 269315. MR 29 #3774. MR 0166499 (29:3774)
 [2]
 A. J. Chorin, "A numerical method for solving incompressible viscous flow problems," J. Computational Physics, v. 2, 1967, p. 12.
 [3]
 J. O. Wilkes, "The finite difference computation of natural convection in an enclosed cavity," Ph.D. Thesis, Univ. of Michigan, Ann Arbor, Mich., 1963.
 [4]
 A. A. Samarskiĭ, "An efficient difference method for solving a multidimensional parabolic equation in an arbitrary domain," Z. Vyčisl. Mat. i Mat. Fiz., v. 2, 1962, pp. 787811 = U.S.S.R. Comput. Math, and Math. Phys., v. 1963, 1964, no. 5, pp. 894926. MR 32 #609. MR 0183127 (32:609)
 [5]
 R. Varga, Matrix Iterative Analysis, PrenticeHall, Englewood Cliffs, N. J., 1962. MR 0158502 (28:1725)
 [6]
 P. R. Garabedian, "Estimation of the relaxation factor for small mesh size," Math. Comp., v. 10, 1956, pp. 183185. MR 19, 583. MR 0088802 (19:583a)
 [7]
 C. E. Pearson, "A computational method for time dependent two dimensional incompressible viscous flow problems," Report No. SRRCRR6417, Sperry Rand Research Center, Sudbury, Mass., 1964.
 [8]
 A. J. Chorin, "The numerical solution of the NavierStokes equations for incompressible fluid," AEC Research and Development Report No. NYO148082, New York Univ., Nov. 1967. MR 0216814 (35:7643)
 [9]
 S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Internat. Series of Monographs on Physics, Clarendon Press, Oxford, 1961. MR 23 #1270. MR 0128226 (23:B1270)
 [10]
 A. J. Chorin, "Numerical study of thermal convection in a fluid layer heated from below," AEC Research and Development Report No. NYO148061, New York Univ., Aug. 1966.
 [11]
 P. H. Rabinowitz, "Nonuniqueness of rectangular solutions of the Benard problem," Arch. Rational Mech. Anal. (To appear.)
 [12]
 E. L. Koschmieder, "On convection on a uniformly heated plane," Beitr. Physik. Alm., v. 39, 1966, p. 1.
 [13]
 H. T. Rossby, "Experimental study of Benard convection with and without rotation," Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, Mass., 1966.
 [14]
 F. Busse, "On the stability of two dimensional convection in a layer heated from below," J. Math. Phys., v. 46, 1967, p. 140.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718196802423922
PII:
S 00255718(1968)02423922
Article copyright:
© Copyright 1968 American Mathematical Society
