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1 Applied Mechanics and Engineering

1 1999

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Tests on a new method for numerical solution to the Navier-Stokes equations*. Part I: plane unsteady flow in finite, rectangular domains

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Klonowska M. E. , Kołodziejczyk M.

1999

tom Vol. 4, no 2

311-339

The paper deals with a new method (Prosnak and Kosma, 1991) for the determination of unsteady, plane flows of viscous incompressible fluids. The characteristic feature of the method consists in elimination of pressure from the system of the Navier-Stokes equations governing the flow - in such a manner that the order of the resulting system is not increased in comparison with the original one. Furthermore, the mathematical problem posed for the resulting system is reduced in the frame of the method to an initial problem for a system of first order ordinary differential equations, wherein time represents the only independent variable. The nonlinearities of the Navier-Stokes equations do not cause any difficulties by virtue of such an approach. In this paper, the method has been applied to flows in plane, finite rectangular domains, and domains composed of rectangles. Numerical solutions to such problems are presented in the paper in graphical form, and some conclusions are drawn concerning the results as well as the method.