Enhancing Material Boundary Visualizations in 2D Unsteady Flow through Local Reference Frame Transformations

Abstract

We present a novel technique for the extraction, visualization, and analysis of material boundaries and Lagrangian coherent structures (LCS) in 2D unsteady flow fields relative to local reference frame transformations. In addition to the input flow field, we leverage existing methods for computing reference frames adapted to local fluid features, in particular those that minimize the observed time derivative. Although, by definition, transforming objective tensor fields between reference frames does not change the tensor field, we show that transforming objective tensors, such as the finite-time Lyapunov exponent (FTLE) or Lagrangian-averaged vorticity deviation (LAVD), or the second-order rate-of-strain tensor, into local reference frames that are naturally adapted to coherent fluid structures has several advantages: (1) The transformed fields enable analyzing LCS in space-time visualizations that are adapted to each structure; (2) They facilitate extracting geometric features, such as iso-surfaces and ridge lines, in a straightforward manner with high accuracy. The resulting visualizations are characterized by lower geometric complexity and enhanced topological fidelity. To demonstrate the effectiveness of our technique, we measure geometric complexity and compare it with iso-surfaces extracted in the conventional reference frame. We show that the decreased geometric complexity of the iso-surfaces in the local reference frame, not only leads to improved geometric and topological results, but also to a decrease in computation time.