Existing methods for analyzing separation of streamlines are often restricted to a finite time or a local area. In our paper we introduce a new method that complements them by allowing an infinite-time-evaluation of steady planar vector fields. Our algorithm unifies combinatorial and probabilistic methods and introduces the concept of separation in time-discrete Markov-Chains. We compute particle distributions instead of the streamlines of single particles. We encode the flow into a map and then into a transition matrix for each time direction. Finally, we compare the results of our grid-independent algorithm to the popular Finite-Time-Lyapunov-Exponents and discuss the discrepancies.

Abstract We present an algorithm that allows stream surfaces to recognize and adapt to vector field topology. Standard stream surface algorithms either refine the surface uncontrolled near critical points which slows down the computation considerably and may lead to a poor surface approximation. Alternatively, the concerned region is omitted from the stream surface by severing it into two parts thus generating an incomplete stream surface. Our algorithm utilizes topological information to provide a fast, accurate, and complete triangulation of the stream surface near critical points. The required topological information is calculated in a preprocessing step. We compare our algorithm against the standard approach both visually and in performance.