Interdisciplinary Centre for Scientific Computing

University of Heidelberg

Im Neuenheimer Feld 368

69120 Heidelberg

Germany

Abstract

The use of multigrid methods in conjunction with a Large Eddy Simulation (LES) is very
proximate since both are based on multiple scales. LES is a turbulence model
which resolves large turbulent scales and models the small ones. The scale
separation is performed by applying a spacial convolution operator (filter
operator) to the
incompressible Navier-Stokes equations. As filter operator a top hat filter is
applied with a grid dependent support size. Hence the application of the
filter results in a locally varying
average in space. The LES model itself also depends on the grid size since
the filtering process removes all subgrid scales. Some special dynamic LES models have been developed by various researchers
which apply two filters with different support size at each point of the
domain to the gouverning equation system. By comparison of the two different large scale
resolutions the model term can be specified locally. This is similar to the
multigrid cycle where the defect is restricted to the coarser grid and higher
frequencies are removed.
Another property of dynamic models is their ability to adjust themselves to
local flow structures. This adaptivity is very useful since in some regions of the domain the
flow can be laminar and a turbulence model is not necessary at all. Hence
dynamic models were used in the simulations.

A Krylov subspace method with linear multigrid as preconditioner is used to solve the linearized system. Within the multigrid cycle it is important to separate modelling and solving in the sense that only on the finest grid the modeled part of the equations is determined as described above. This is necessary for an appropriate modelling of the subgrid turbulent scales. Afterwards the model term is restricted to the coarse grids and a standard linear multigrid cycle can be used. This solution strategy was applied to different flow problems which will be presented.