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Math. Comput. Appl. 2006, 11(2), 127-136; doi:10.3390/mca11020127

On the Numerical Solution of the Incompressible Navier-Stokes Equations in Primitive Variables Using Grid Generation Techniques

Department of Mathematics, Faculty of Science,Suez Canal University, Ismailia, Egypt
Published: 1 August 2006
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Abstract

In this paper presents a new model procedure for the solution of the incompressible Navier-Stokes equations in primitive variables, using grid generation techniques. The time dependent momentum equations are solved explicitly for the velocity field using the explicit marching procedure, the continuity equation is implied at each grid point in the solution of pressure equation, while the SOR method is used for the Neumann problem for pressure. Results obtained for the model problem of driven flow in a square cavity demonstrate that the method yields accurate solutions. The results of the numerical computations in a driven cavity, which are presented for the history of the residues at several Reynolds numbers Re=100,1000,4000 and 5000 all the computed results are obtained without any artificial dissipation. This feature of the present procedure demonstrates its excellent convergence and stability characteristics. Numerically results obtained for the steady state static pressure in the driven cavity are presented for the first time at Re=4000 and 5000 using non-staggered grid.
Keywords: successive over-relaxation iteration; Navier-Stokes equations; driven cavity flows successive over-relaxation iteration; Navier-Stokes equations; driven cavity flows
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Salem, S.A. On the Numerical Solution of the Incompressible Navier-Stokes Equations in Primitive Variables Using Grid Generation Techniques. Math. Comput. Appl. 2006, 11, 127-136.

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Math. Comput. Appl. EISSN 2297-8747 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
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