Enhancement of Streamline Upwinding Finite Element Solutions by Adaptive Meshing Technique

Abstract

A finite element method for analysis of two-dimensional, steady-state, viscous incompressible flow is presented. Finite element equations are derived from a set of coupled nonlinear Navier-Stokes equations that consists of the conservation of mass and momentums. The convection terms in momentum equations are treated by streamline upwinding method to avoid the oscillation in the solution. The method has been developed for triangular element that employs equal-order interpolation functions for both the velocities and pressure. A segregated solution algorithm is also incorporated to compute the velocities and pressure separately. The method is combined with an adaptive meshing technique to further increase the solution accuracy, and at the same time, to minimize the computational time and computer memory requirement. The finite element formulation and the computer program have been verified by several examples that have known solutions prior to applying to solve more complex flow problems.