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.
Highlights
We shall describe a combination of numerical grid generation techniques using stretching function by Marcel Vinkur [9] for solving the incompressible Navier-Stokes equations in primitive variables. , As an illustration, use them to compute driven cavity flows
To computational domain is introduced this transformation is accomplished by specifying a generalized coordinate system which will map the nonrectangular grid system in the physical domain to rectangular uniform grid spacing in the computational domain
A method of controlling the spacing of the coordinate lines given by Middlecoff [8] has been domain in the square cavity in order to treat higher Reynolds number flow, since the coordinate lines must concentrate near the surface to a greater degree as the Reynolds number increases
Summary
We shall describe a combination of numerical grid generation techniques using stretching function by Marcel Vinkur [9] for solving the incompressible Navier-Stokes equations in primitive variables. , As an illustration, use them to compute driven cavity flows. We shall describe a combination of numerical grid generation techniques using stretching function by Marcel Vinkur [9] for solving the incompressible Navier-Stokes equations in primitive variables. A numerical method using the primitive variables (u, v, p) to solve the Navier-Stokes equations are given by Ghia [1] and S.Abdallah [2]. A method of controlling the spacing of the coordinate lines given by Middlecoff [8] has been domain in the square cavity in order to treat higher Reynolds number flow, since the coordinate lines must concentrate near the surface to a greater degree as the Reynolds number increases. In the present study, the model problem of driven flow in a square cavity is investigated using the primitive variables (u, v, p) using grid generation technique. Results for velocity as well as pressure fields are obtained for Reynolds number Re ranging from 100 to 5000 and are compared with those of the (ω,ψ) system and (u, v, p) system without grid generation technique
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