On Optimal AMLI Solvers for Incompressible Navier-Stokes Problems
Abstract
We consider the incompressible Navier-Stokes problem and a projection scheme based on Crouzeix-Raviart finite element approximation of the velocities and piece-wise constant approximation of the pressure. These non-conforming 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 time-stepping solution method. The algorithm for the Navier-Stokes problem has a total computational complexity of optimal order. We present numerical tests for the efficiency of the AMLI solvers for the case of lid-driven 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:
-
- Navier-Stokes equations;
- finite element analysis;
- boundary-value problems;
- Galerkin method;
- matrix algebra;
- 47.10.ad;
- 47.11.Fg;
- 41.20.Gz;
- 02.70.Dh;
- 02.10.Yn;
- Navier-Stokes equations;
- Finite element methods;
- Magnetostatics;
- magnetic shielding magnetic induction boundary-value problems;
- Finite-element and Galerkin methods;
- Matrix theory