Solution of the incompressible Navier Stokes equations with ILU preconditioned Krylov subspace methods

M. ur Rehman, C. Vuik and G. Segal

Email: M.urRehman@ewi.tudelft.nl

Faculty of Electrical Engineering, Mathematics and Computer Science, Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands.

In this paper, the incompressible Stokes and Navier Stokes problems are solved in a square and backward facing step domain with an ILU preconditioned Krylov solver. 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. Results are done with ILU preconditioned GMRES and BiCGSTAB. It is observed that our schemes converges rapdily for both Picard’s and Newton’s linearization for Navier Stokes problem. Numerical experiments are performed in a 2-D domain for various finite element discretization schemes.