HLRB Project pr74ne

Parallel multigrid methods for non-linear, time-dependent incompressible fluid flow

Lehrstuhl für Numerische Mathematik,TUM

Parallel multigrid methods for non-linear, time-dependent incompressible fluid flow

Lehrstuhl für Numerische Mathematik,TUM

Lehrstuhl für Numerische Mathematik,TUM

Daniel Drzisga

Boltzmannstr. 3

85748 Garching

We consider robust multigrid methods for the Stokes equations on hierarchical hybrid grids (HHG). The special design of the method, i.e., a compromise of structured and unstructured grids, fits the flexibility of finite elements and the efficiency of geometric multigrid methods. In particular, so-called all at once solution techniques will be studied which are based on Uzawa-type smoothers. These have been found to be an attractive choice, since they are numerically cheap and can be implemented with only nearest-neighbour communication.Our aim is to develop parallel solution strategies for the simulation of incompressible fluid flow and its coupling to a transport equation for the concentration. These problems appear for instance when diluted polymeric fluids are studied. The physical process can be described by the incompressible generalized Navier–Stokes equations coupled with a convection–diffusion equation. As a part of the SPPEXA project TERRA-NEO we also aim to study non-linear problems with application in geodynamics. Here, the non-linearity is usually introduced via a velocity and temperature dependent viscosity. The influence of linear- and non-linear models are investigated by high resolution simulations using real data.The efficiency of the implementation and methodology is illustrated by various large scale simulations and scaling experiments.

Impressum, Conny Wendler