Multiscale visualization techniques for static as well as time-dependent flow
fields are indispensable tools for the understanding and analysis of complex flow
phenomena. The methods presented in [2, 18] generate multiscale visualizations
and they are based on an anisotropic diffusion, resp., anisotropic transport diffusion
operator. However, the presented discretizations are only given on quadtree or
octree grids, which in general are impracticable in real applications for Computational
Fluid Dynamics (CFD). In this work, we extend these methods in [2] and we
discuss robust and accurate FEM discretization and iterative solver techniques on
unstructured quadrilateral grids. Thus, undesirable numerical diffusion as well as
numerical oscillations are avoided and efficiency of the numerical implementation
is ensured. Together with improved blending strategies the effective visualization
of complex flow fields in 2D is possible.