Annette Stephansen
Centre for Integrated Petroleum Research
Bergen, Norway
Streamline tracing on irregular grids requires reliable
interpolation of velocity fields. We propose a new method for direct
streamline tracing on polygon and polytope cells. While some
numerical methods provide a basis function that can be used for
interpolation, other methods provide only the fluxes at the faces of
the elements. We introduce the concept of full field and raw field
methods. Full field methods have built-in interpolation, but are
often not defined on general grids such as polygonal and polyhedral
grids which we examine here. Also, reliability issues may arise on
non-simplicial meshes in terms of not being able to reproduce
constant velocity fields. We propose an interpolation in H(div) and
H(curl) valid on general grids that is based on barycentric
coordinates and that reproduces uniform flow. The interpolation can
be used to compute the streamline directly on the complex cell
geometry. The method generalizes to convex polytopes in 3D, with a
restriction on the polytope topology near corners that is shown to
be satisfied by several popular grid types. Numerical results
confirm that the method is applicable to general grids and preserves
uniform flow.
The work is done in collaboration with R. A. Klausen at CMA, University of Oslo, and A. F. Rasmussen at Sintef.