DELFT UNIVERSITY OF TECHNOLOGY REPORT 06-05 Solution of the incompressible Navier Stokes equations with preconditioned Krylov subspace methods

In this report, using SEPRAN [1], the incompressible Stokes and Navier Stokes problems are solved in a square and L-shaped domain with a varying grid size and Reynolds number. Both problems are solved with iterative solvers using an ILU preconditioner. Different ordering techniques of the grid points and the unknowns are used to avoid breakdown of the LU decomposition. These ordering techniques used with ILU preconditioning makes that the iterative methods applied to the system of equations converge rapidly. With the reordering techniques, a direct solver can be used to solve the coupled system without pivoting. Numerical experiments are performed in a 2-D and 3-D domain using various finite element discretization schemes.