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1 International Journal of Applied Mechanics and Engineering

1 2002

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Tests on a new method for numerical solution to the Navier-Stokes equations. part II: plane unsteady flow around curvilinear contours

Klonowska-Prosnak M. E., Kołodziejczyk M.

International Journal of Applied Mechanics and Engineering

2002

Vol. 7, no 2

619-652

Similarly as the preceding paper of the authors (Klonowska and Kołodziejczyk, 1999) also the present one deals with the new method (Prosnak and Kosma, 1991) for the determination of unsteady, plane flows of viscous incompressible fluids. The novelty of the method consists in elimination of pressure from the system of the Navier-Stokes equations by means of integration of the "total" differential of pressure. Consequently - the order of the system resulting from such an elimination is not increased in comparison with the original one, and no artificial, non-physical boundary conditions occur. The main difference between the present paper and the previous one consists in geometrical properties of the domain of solution. It is infinite, and bounded by a curvilinear contour. Three contours are considered in the paper: a flat plate, a circle, and the NACA 0012 airfoil. The results prove, that also in these cases the method works properly - at least for rather small values of the Reynolds number. Such a limitation is due to the efficiency of the computers being available at the time, when the calculations were made.