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Numerical solution of the Navier-Stokes equations


Author: Alexandre Joel Chorin
Journal: Math. Comp. 22 (1968), 745-762
MSC: Primary 65.68
DOI: https://doi.org/10.1090/S0025-5718-1968-0242392-2
MathSciNet review: 0242392
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Abstract: A finite-difference method for solving the time-dependent 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 three-dimensional convection problem is presented.


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  • [1] H. Fujita & T. Kato, "On the Navier-Stokes initial value problem. I," Arch. Rational Mech. Anal., v. 16, 1964, pp. 269-315. 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 multi-dimensional parabolic equation in an arbitrary domain," Z. Vyčisl. Mat. i Mat. Fiz., v. 2, 1962, pp. 787-811 = U.S.S.R. Comput. Math, and Math. Phys., v. 1963, 1964, no. 5, pp. 894-926. MR 32 #609. MR 0183127 (32:609)
  • [5] R. Varga, Matrix Iterative Analysis, Prentice-Hall, 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. 183-185. 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. SRRC-RR-64-17, Sperry Rand Research Center, Sudbury, Mass., 1964.
  • [8] A. J. Chorin, "The numerical solution of the Navier-Stokes equations for incompressible fluid," AEC Research and Development Report No. NYO-1480-82, 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. NYO-1480-61, 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: https://doi.org/10.1090/S0025-5718-1968-0242392-2
Article copyright: © Copyright 1968 American Mathematical Society

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