Stream-Vorticity function finite element computational fluid dynamics

In many design projects, the design will depend on the fluid flow through it. Since many different geometries may be analyzed, any computational method must be able to quickly and easily handle these changes. Finite element methods offered this ability to quickly and easily change geometery. However, the method has not been as widely used for fluid dynamics as finite difference methods,

A finite element method for the stream-vorticity function is developed. In addition, a method for applying the physical fluid boundary conditions for a solid wall is developed. The method is tested using the driven cavity. The results from these tests showed very good agreement with much finer mesh finite difference methods. Finally, the new method is applied to a complex internal geometry and results are shown.