On preconditioning incompressible non-Newtonian flow problems

This paper deals with fast and reliable numerical solution methods for the incompressible non-Newtonian Navier-Stokes equations. To handle the nonlinearity of the governing equations, the Picard and Newton methods are used to linearize these coupled partial differential equations. For space discretization we use the finite element method and...

Comparison of some preconditioners for the incompressible Navier-Stokes equations

In this report we explore the performance of the SIMPLER , augmented Lagrangian, ’grad-div’ preconditioners and their variants for the two-by-two block systems arising in the incompressible Navier-Stokes equations. The lid-driven cavity and flow over a finite flat plate are chosen as the benchmark problems. For each problem Reynolds number...

Combining the Augmented Lagrangian Preconditioner withe the SIMPLE Schur Complement Approximation

The augmented Lagrangian (AL) preconditioner and its variant have been successfully applied to solve saddle point systems arising from the incompressible Navier-Stokes equations discretized by the finite element method. Attractive features are the purely algebraic construction and robustness with respect to the Reynolds number and mesh renement....

Efficient and robust Schur complement approximations in the augmented Lagrangian preconditioner for the incompressible laminar flows

This paper introduces three new Schur complement approximations for the augmented Lagrangian preconditioner. The incompressible Navier-Stokes equations discretized by a stabilized finite element method are utilized to evaluate these new approximations of the Schur complement. A wide range of numerical experiments in the laminar context...