KOPFEM – Code API and Extrapolation Schemes

Nowadays, despite the variety of commercial solvers available on the market, the question of the design and development of effective numerical solvers is still open. It is a fact that many problems can not fi nd their proper treatment using the existing (commercial) codes. Typical examples are large sized problems with complicated geometry, e.g. problems in micromechanics, which necessarily require a parallel execution. In this sense, a specifi c-purpose in-house code, specially designed and programmed for a particular parallel architecture, can often provide much better performance than the existing general-purpose tools.

MpCCI Interface for DDFEm code

The parallel 3D-elasticity solver DDFEM is an example for such an in-house development, undertaken to meet the needs of certain macro- and micromechanical problems. "DD" in the name stays for "domain decomposition" - this is the method for parallelizing the numerics. First and second order hierarchical local approximations are employed within tetrahedral finite elements - because the latter are appropriate for automatic mesh generation, providing at the same time a good approximation for complicated geometries. Recently DDFEM has been extended to tackle heat problems as well.

The MpCCI driver for DDFEM is a new development also, which makes possible to use DDFEM in FSI simulations employing the so called weak coupling. Note, that in some observable future it is rather not very probable some general-purpose (commercial) package with strong coupling between the flow- and solid solvers to appear. Therefore, tolls like MpCCI, technically facilitating and intermediating the weak-coupling approaches, are indispensable.

Extrapolation Schemes for incompatible Geometries

The MpCCI interpolation algorithms are based on the assumption that both coupled surfaces are well defined and geometrically compatible to each other. The CFD and FEM domain can be modelled individually based on accuracy and runtime demands. MpCCI then is responsible to map the discretisations used in CFD and FEM to each other. However, in some cases it might happen that parts which are modelled in detail in the FEM domain are not represented in the coupled CFD domain. In the figure above the pipe is only part of the FEM model – and not of the CFD model.

To handle such model mismatches a method is needed for assigning data and thus emulating a coupling for this pipe region. One way is to assign default values. This leads to a number of problems from listing all regions up to guessing values for each region. Therefore MpCCI was extended to deal automatically with non matched regions by extrapolating values from matched regions into the non matched ones. The extrapolation is based on a weighting function over the distances to the borders of the non matched region.

Project Partner

Project Weblink:

Fraunhofer Institut für Techno- und Wirtschaftsmathematik ITWM

www.itwm.fraunhofer.de/en/hpc__parallelisierung__ddfem/ddfem/

Fraunhofer Institut SCAI

www.scai.fhg.de/sian