Inertial Steady 2D Vector Field Topology

Abstract

Vector field topology is a powerful and matured tool for the study of the asymptotic behavior of tracer particles in steady flows. Yet, it does not capture the behavior of finite-sized particles, because they develop inertia and do not move tangential to the flow. In this paper, we use the fact that the trajectories of inertial particles can be described as tangent curves of a higher dimensional vector field. Using this, we conduct a full classification of the first-order critical points of this higher dimensional flow, and devise a method to their efficient extraction. Further, we interactively visualize the asymptotic behavior of finite-sized particles by a glyph visualization that encodes the outcome of any initial condition of the governing ODE, i.e., for a varying initial position and/or initial velocity. With this, we present a first approach to extend traditional vector field topology to the inertial case.