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Convergence of coupled elliptic equations for separated flow problem

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Il Nuovo Cimento B (1971-1996)

Summary

An overrelaxation procedure, that includes accelerating parameters is applied to the coupled elliptic equations in order to reduce the computational time. The specific system is the finite-difference form of the Navier-Stokes equations for separated flow in a symmetric sudden-expansion channel. The convergence domain for the successive overrelaxation method and the values of accelerating parameters which allow one to choose optimum values in this domain are given. Numerically solutions are obtained for Reynolds numbers up to 2000. Reduction in computing time by a factor of 4 is obtained by using the optimum values of accelerating parameters.

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Abbreviations

H :

upstream channel height

h :

size of the square mesh

U 0 :

average upstream channel velocity

X, Y :

nondimensional Cartesian coordinates

u,v :

nondimensionalx andy velocities components

ψ:

nondimensional stream function

w :

nondimensional vorticity function

r :

relaxation factor

r ψ :

overrelaxation factor for stream function

r w :

overrelaxation factor for vorticity function

D ψ :

damping parameter for stream function

D w :

damping parameter for vorticity function

Re :

Reynolds number

References

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  3. M. Friedman:J. Eng. Math.,9, 285 (1972).

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  4. M. Nallasamy andK. K. Prasad:Numerical investigation of laminar heat transfer in step induced internal separated flows, Paper No.7,Proceedings of First National Heat and Mass Transfer Conference, Madras, India (1971).

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  6. M. Nallasamy andK. Prasad:Flow and heat transfer in internal laminar separated region, to be published.

  7. D. Greenspan:Discrete Numerical Methods in Physics and Engineering (AcademicPress, New York, N.Y., 1974).

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Authors and Affiliations

  1. Mosul University, Mosul, Iraq

    M. F. Mosa & N. N. Abdulla

Authors
  1. M. F. Mosa
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  2. N. N. Abdulla
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Mosa, M.F., Abdulla, N.N. Convergence of coupled elliptic equations for separated flow problem. Nuov Cim B 105, 1081–1089 (1990). https://doi.org/10.1007/BF02827317

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  • DOI: https://doi.org/10.1007/BF02827317

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