  A robust finite volume method for viscoelastic flow analysis on general
unstructured meshes is developed. It is built upon a general-purpose
stabilization framework for high Weissenberg number flows. The numerical
framework provides full combinatorial flexibility between different kinds of
rheological models on the one hand, and effective stabilization methods on the
other hand. A special emphasis is put on the velocity-stress-coupling on
co-located computational grids. Using special face interpolation techniques, a
semi-implicit stress interpolation correction is proposed to correct the
cell-face interpolation of the stress in the divergence operator of the
momentum balance. Investigating the entry-flow problem of the 4:1 contraction
benchmark, we demonstrate that the numerical methods are robust over a wide
range of Weissenberg numbers and significantly alleviate the high Weissenberg
number problem. The accuracy of the results is evaluated in a detailed mesh
convergence study.
