Mass‐Dependent Integral Curves in Unsteady Vector Fields

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Figure 1: Visualization of inertial critical points and a glyph-based visualization of the asympotic behavior of inertial particles. The sink (blue critical point) that is reached by an inertial particle depends on its initial position x 0 and the initial velocity v 0 . The glyph location encodes x 0 and the glyph disc color-codes the sink that is reached for a certain v 0 . The glyph center represents v 0 = 0 and the selected glyph is enlarged in the bottom right corner, showing the seeds of inertial particle trajectories. Left: BORROMEAN RINGS with particle diameter dp = 70 µm and maximal velocity vmax = 10 m/s (occurs at glyph boundary), middle: DUFFING OSCILLATOR with dp = 100 µm, vmax = 5 m/s, and right: NINE CP with dp = 70 µm, vmax = 10 m/s. Inertial critical point types are listed in Table 1. AbstractVector 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.

Section: Inertial Particles In Visualizationmentioning

confidence: 99%

Inertial Steady 2D Vector Field Topology

Günther¹,

Theisel²

2016

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“…To abstract from the underlying equations of motion, Günther et al [GKKT13] extended the concept of flow map φ (cf. [Hal01,SLM05]) to inertial particles.…”

Section: Mass-dependent Flow Mapmentioning

confidence: 99%

“…Using the mass-dependent flow map notation, integral curves have been extended in [GKKT13] for inertial particles. Using the mass-dependent flow map notation, integral curves have been extended in [GKKT13] for inertial particles.…”

Section: Inertial Particles In Visualizationmentioning

confidence: 99%

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Finite‐Time Mass Separation for Comparative Visualizations of Inertial Particles

Günther¹,

Theisel²

2015

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dp : 20 µm 200 µm x y t t τ ε Arclength (r) τ 0 20 0 2.5 Figure 1: Mass separation of inertial particles in the DOUBLE GYRE. Left image: Mass (color-coded) that separates strongest during integration over time τ = 17. Center image: inertial particles of different mass are released at the cross in the left image.In space-time their trajectories assemble a surface, with the purple line being its frontline-a so-called massline. The green line is the particle trajectory with strongest separation (here, with diameter dp = 99 µm). Right image: plot of difference to reference particle, here the smallest inertial particle (diameter dp = 20 µm), which makes the temporal evolution of the separation apparent. AbstractThe visual analysis of flows with inertial particle trajectories is a challenging problem because time-dependent particle trajectories additionally depend on mass, which gives rise to an infinite number of possible trajectories passing through every point in space-time. This paper presents an approach to a comparative visualization of the inertial particles' separation behavior. For this, we define the Finite-Time Mass Separation (FTMS), a scalar field that measures at each point in the domain how quickly inertial particles separate that were released from the same location but with slightly different mass. Extracting and visualizing the mass that induces the largest separation provides a simplified view on the critical masses. By using complementary coordinated views, we additionally visualize corresponding inertial particle trajectories in space-time by integral curves and surfaces. For a quantitative analysis, we plot Euclidean and arc length-based distances to a reference particle over time, which allows to observe the temporal evolution of separation events. We demonstrate our approach on a number of analytic and one real-world unsteady 2D field.

“…The second unsteady sequence captures the simulation of the flow regime around a helicopter in slow forward flight close to the ground. The data by Kutz et al [KKKK12] was studied for brown-out conditions [GKKT13]. Fig.…”

Section: Visualization Of Steady and Time-dependent Datamentioning

confidence: 99%

Hierarchical opacity optimization for sets of 3D line fields

Günther¹,

Rössl²,

Theisel³

2014

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Figure 1: View-dependent, frame-coherent and interactive selection of meaningful lines for sets of line fields: pathlines (left, 58 ms/opacity update) and streaklines (right, 78 ms/opacity update) in a cylinder flow. AbstractThe selection of meaningful lines for 3D line data visualization has been intensively researched in recent years. Most approaches focus on single line fields where one line passes through each domain point. This paper presents a selection approach for sets of line fields which is based on a global optimization of the opacity of candidate lines. For this, existing approaches for single line fields are modified such that significantly larger amounts of line representatives are handled. Furthermore, time coherence is addressed for animations, making this the first approach that solves the line selection problem for 3D time-dependent flow. We apply our technique to visualize dense sets of pathlines, sets of magnetic field lines, and animated sets of pathlines, streaklines and masslines. This is the authors preprint. The definitive version is available at