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• EFFICIENT NUMERICAL CALCULATION OF UNSTEADY FREE CONVECTION  download article

Graham de Vahl Davis
University of NSW

Eddie Leonardi
Computational Fluid Dynamics Research Laboratory, School of Mechanical and Manufacturing Engineering, The University of New South Wales, Sydney, Australia 2052

Victoria Timchenko
University of New South Wales

Micha Wolfshtein
Faculty of Aerospace Engineering, Technion - Israel Institute of technology, Haifa, Israel

ABSTRACT

The solution of Poisson equations is an important ingredient of most methods for the solution of the incompressible Navier-Stokes equations. In this paper we report on an empirical study of three traditional methods, namely the Successive Over Relaxation (SOR), the Alternating Directions Implicit (ADI) and the Conjugate-Gradients (CG) methods. The boundary conditions considered are typical to vorticity-vector potential methods, and the discretization is by second order central differences on a Cartesian homogeneous mesh. An over-relaxation parameter for the SOR method and a time step have to be determined. However, such parameters do not depend on the solution, only on the matrix to be inverted. Therefore they can be determined empirically for a given matrix. This makes these methods attractive for time dependent problems. In this paper this is done by trial and error. The results show that these three conventional methods can be used efficiently for such problems. It is also seen that the ADI method is superior to the other two, both in processor time and in number of iterations. Moreover, it appears that the ADI method does not need more time steps for larger meshes, while the two other methods require more iterations or time steps.

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