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To improve existing weather prediction and reanalysis capabilities, high-resolution and multi-modal climate data becomes an increasingly important topic. The advent of increasingly dense numerical simulation of atmospheric phenomena, provides new means to better understand dynamic processes and to visualize structural flow patterns that remain hidden otherwise. In the presented illustrations we demonstrate an advanced technique to visualize multiple scales of dense flow fields and Lagrangian patterns therein, simulated by state-of-the-art simulation models for each scale. They provide a deeper insight into the structural differences and patterns that occur on each scale and highlight the complexity of flow phenomena in our atmosphere.
To improve existing weather prediction and reanalysis capabilities, high-resolution and multi-modal climate data becomes an increasingly important topic. The advent of increasingly dense numerical simulation of atmospheric phenomena, provides new means to better understand dynamic processes and to visualize structural flow patterns that remain hidden otherwise. In the presented illustrations we demonstrate an advanced technique to visualize multiple scales of dense flow fields and Lagrangian patterns therein, simulated by state-of-the-art simulation models for each scale. They provide a deeper insight into the structural differences and patterns that occur on each scale and highlight the complexity of flow phenomena in our atmosphere.
This paper is associated with a poster winner of a 2016 APS/DFD Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available from the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2016.GFM.P0030
Traditionally, Lagrangian fields such as finite-time Lyapunov exponents (FTLE)
are precomputed on a discrete grid and are ray casted afterwards. This, however,
introduces both grid discretization errors and sampling errors during ray marching.
In this work, we apply a progressive, view-dependent Monte Carlo-based approach
for the visualization of such Lagrangian fields in time-dependent flows. Our ap-
proach avoids grid discretization and ray marching errors completely, is consistent,
and has a low memory consumption. The system provides noisy previews that con-
verge over time to an accurate high-quality visualization. Compared to traditional
approaches, the proposed system avoids explicitly predefined fieldline seeding
structures, and uses a Monte Carlo sampling strategy named Woodcock tracking
to distribute samples along the view ray. An acceleration of this sampling strategy
requires local upper bounds for the FTLE values, which we progressively acquire
during the rendering. Our approach is tailored for high-quality visualizations of
complex FTLE fields and is guaranteed to faithfully represent detailed ridge surface
structures as indicators for Lagrangian coherent structures (LCS). We demonstrate
the effectiveness of our approach by using a set of analytic test cases and real-world numerical simulations.
Lagrangian Coherent Structures (LCS) have become a widespread and powerful method to describe dynamic motion patterns in time-dependent flow fields. The standard way to extract LCS is to compute height ridges in the Finite Time Lyapunov Exponent (FTLE) field. In this work, we present an alternative method to approximate Lagrangian features for 2D unsteady flow fields that achieves subgrid accuracy without additional particle sampling. We obtain this by a geometric reconstruction of the flow map using additional material constraints for the available samples. In comparison to the standard method, this allows for a more accurate global approximation of LCS on sparse grids and for long integration intervals. The proposed algorithm works directly on a set of given particle trajectories and without additional flow map derivatives. We demonstrate its application for a set of computational fluid dynamic examples, as well as trajectories acquired by Lagrangian methods, and discuss its
benefits and limitations.