On the Application of the Finite Element Method to Three-Dimensional Incompressible Potential Flow

Abstract

<p>This thesis describes the application of the finite element method to three-dimensional potential flow. The flow is assumed to be steady and incompressible. The flow region is simply connected and has complicated geometric boundaries. The boundary condition is of the Neumann type, or mixed Dirichlet-Neumann type. The finite element method presented provides an economical solution for the problem which could be difficult to solve using other methods.</p> <p>A versatile computer program was developed and used for solving three specific problems of flow around bends. One of the three problems had a known two-dimensional exact solution. The results obtained for this problem are in good agreement with its exact solution. The computer program can be utilized to solve similar problems, subject to the same governing equations and boundary conditions, in related fields such as electrostatics and heat conduction.</p>