Abstract
A method is presented for solution of the Navier-Stokes equations in an extremal formulation based on a joint application of Pontryagin's maximum principle and a representation of the unknown functions in the form of power series.
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Abbreviations
- x, y:
-
space coordinates
- t:
-
time
- u, v:
-
horizontal and vertical components of velocity
- P:
-
pressure
- Re:
-
Reynolds number
- γ:
-
boundary of region
- un :
-
projection of velocity vector on normal to boundary of region
- s:
-
arc length of integration contour
- tk :
-
finite time instant
- m, ℓ:
-
number of grid nodes
- M, L:
-
parameters determining the number of nodes of a gridwork
- n, k:
-
power series indices
- J0 :
-
minimizing functional
- U, V:
-
conjugate functions
- α:
-
step multiplier of the conjugate gradient method
- p:
-
iteration number
Literature cited
P. J. Roache, Computational Hydronamics, Prentice-Hall (1976).
A. A. Shmukin, Applied Problems in the Aerodynamics of Aircraft [in Russian], Kiev (1984), pp. 87–93.
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mischenko, Mathematical Theory of Optical Processes [in Russian], Moscow (1983).
O. M. Alifanov, Identification of Aircraft Heat Exchange Processes [in Russian], Moscow (1979).
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 5, pp. 730–735, May, 1989.
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Shmukin, A.A., Posudievskii, R.A. Gradient numerical-analytical method for solution of the navier-stokes equations for a viscous incompressible fluid. Journal of Engineering Physics 56, 512–515 (1989). https://doi.org/10.1007/BF01297596
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DOI: https://doi.org/10.1007/BF01297596