Iterative methods for incompressible flow

Abstract

The goal of this thesis is to illustrate the effectiveness of iterative methods on the discretized Navier Stokes equations. The standard lid-driven cavity in both 2-D and 3-D test cases are examined and compared with published results of the same type. The numerical results are obtained by reducing the partial differential equations (PDEs) to a system of algebraic equations with a stabilized P1-P1 Finite Element Method (FEM) in space. Gear's Backward Difference Formula (BDF2) and an adaptive time stepping scheme utilizing a first order Backward Euler (BE) startup and BDF2 are then utilized to discretizc the time derivative of the Javier-Stokes equations. The iterative method used is the Generalized Minimal Residual (GMRES) along with the selected preconditioners Incomplete LU Factorization (ILU), Jacobi preconditioner and the Block Jacobi preconditioner.