Subject: Algebraic Multigrid Methods for the Numerical Solution of the Incompressible Navier-Stokes Equations
Author: Dipl.-Ing. Markus Wabro
Supervisor: A.Univ.Prof. Dipl.-Ing. Dr. Walter Zulehner
Additional Supervisor: O.Univ.Prof. Dipl.-Ing. Dr. Ulrich Langer
External Referee: Prof. Dr. Arnold Reusken
pressure on the surface of the solution of the rotax problem with nu=5.10^-4

If the Navier-Stokes equations for incompressible fluids are linearized using fixed point iterations, the Oseen equations arise. In this thesis we provide concepts for the coupled algebraic multigrid (AMG) solution of this saddle point system, where coupled here is meant in contrast to methods, where pressure and velocity equations are iteratively decoupled, and 'standard' AMG is used for the solution of the resulting scalar problems.

We show how the coarse levels can be constructed (where their stability is an important issue) and which smoothers (known from geometric multigrid methods for saddle point systems) can be used.

main flow of the solution of the rotax problem with nu=5.10^-4

To prove the efficiency of our methods experimentally, we apply them to finite element discretizations of various problems (model problems and also more complex industrial settings) and compare them with classical approaches.


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