An Interpolation Scheme for VDVP Lagrangian Basis Flows

Abstract

Using the Eulerian paradigm, accurate flow visualization of 3D time-varying data requires a high temporal resolution resulting in large storage requirements. The Lagrangian paradigm has proven to be a viable in situ-based approach to tackle this large data visualization problem. However, previous methods constrained the generation of Lagrangian basis flows to the special case of fixed duration and fixed placement (FDFP), in part because reconstructing the flow field using these basis flows is trivial. Our research relaxes this constraint, by considering the general case of variable duration and variable placement (VDVP) with the goal of increasing the amount of information per byte stored. That said, reconstructing the flow field using VDVP basis flows is non-trivial; the primary contribution of our work is a method we call VDVP-Interpolation which solves this problem. VDVP-Interpolation reduces error propagation and limits interpolation error while using VDVP Lagrangian basis flows. As a secondary contribution of the work, we generate VDVP basis flows for multiple data sets and demonstrate improved accuracy-storage propositions compared to previous work. In some cases, we demonstrate up to 40-60% more accurate pathline calculation while using 50% less data storage.