On Optimal AMLI Solvers for Incompressible NavierStokes Problems
Abstract
We consider the incompressible NavierStokes problem and a projection scheme based on CrouzeixRaviart finite element approximation of the velocities and piecewise constant approximation of the pressure. These nonconforming finite elements guarantee that the divergence of the velocity field is zero inside each element, i.e., the approximation is locally conservative.
We propose optimal order Algebraic MultiLevel Iteration (AMLI) preconditioners for both, the decoupled scalar parabolic problems at the prediction step as well as to the mixed finite element method (FEM) problem at the projection step. The main contribution of the current paper is the obtained scalability of the AMLI methods for the related composite timestepping solution method. The algorithm for the NavierStokes problem has a total computational complexity of optimal order. We present numerical tests for the efficiency of the AMLI solvers for the case of liddriven cavity flow for different Reynolds numbers.
 Publication:

Application of Mathematics in Technical and Natural Sciences
 Pub Date:
 November 2010
 DOI:
 10.1063/1.3526645
 Bibcode:
 2010AIPC.1301..457B
 Keywords:

 NavierStokes equations;
 finite element analysis;
 boundaryvalue problems;
 Galerkin method;
 matrix algebra;
 47.10.ad;
 47.11.Fg;
 41.20.Gz;
 02.70.Dh;
 02.10.Yn;
 NavierStokes equations;
 Finite element methods;
 Magnetostatics;
 magnetic shielding magnetic induction boundaryvalue problems;
 Finiteelement and Galerkin methods;
 Matrix theory