The numerical modellings of laminar and turbulent viscous fluid flour

Abstract

The numerical solution of the Navier-Stokes Equations is presented for a two-dimensional incompressible fluid in terms of stream function and vorticity. An uncoupled Galerkin formulation is derived from the governing equations and their respective natural boundary conditions. By assuming a polynomial variation of both unknowns within the flow domain an approximate solution is achieved by the finite element method. In the first part of this work a successful solution of three laminar flow problems is achieved, i.e. the flow: within a square cavity, over a downstream step and past a circular cylinder. Adequate comparison is made with earlier work. In the second part the solution scheme is extended to model developing turbulent flow in a channel by means of an algebraic closure of the time averaged equations. In order to model a variety of flow problems the development of a suitable automatic mesh generating scheme is carried out. Providing fast and efficient discretization of each flow region. This work concentrates on evaluating the solution scheme by solving problems where previous work already exists. With the aid of the mesh generator the program can also be used as a practical predictive tool.

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