Benchmark problems for numerical treatment of backflow at open boundaries.

In computational fluid dynamics, incoming velocity at open boundaries, or backflow, often yields unphysical instabilities already for moderate Reynolds numbers. Several treatments to overcome these backflow instabilities have been proposed in the literature. However, these approaches have not yet been compared in detail in terms of accuracy in different physiological regimes, in particular because of the difficulty to generate stable reference solutions apart from analytical forms. In this work, we present a set of benchmark problems in order to compare different methods in different backflow regimes (with a full reversal flow and with propagating vortices after a stenosis). The examples are implemented in FreeFem++, and the source code is openly available, making them a solid basis for future method developments.