Source Inversion by Forward Integration in Inertial Flows

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dc.contributor.authorGünther, Tobiasen_US
dc.contributor.authorTheisel, Holgeren_US
dc.contributor.editorKwan-Liu Ma and Giuseppe Santucci and Jarke van Wijken_US
dc.date.accessioned2016-06-09T09:32:58Z
dc.date.available2016-06-09T09:32:58Z
dc.date.issued2016en_US
dc.description.abstractInertial particles are finite-sized objects traveling with a certain velocity that differs from the underlying carrying flow, i.e., they are mass-dependent and subject to inertia. Their backward integration is in practice infeasible, since a slight change in the initial velocity causes extreme changes in the recovered position. Thus, if an inertial particle is observed, it is difficult to recover where it came from. This is known as the source inversion problem, which has many practical applications in recovering the source of airborne or waterborne pollutions. Inertial trajectories live in a higher dimensional spatio-velocity space. In this paper, we show that this space is only sparsely populated. Assuming that inertial particles are released with a given initial velocity (e.g., from rest), particles may reach a certain location only with a limited set of possible velocities. In fact, with increasing integration duration and dependent on the particle response time, inertial particles converge to a terminal velocity. We show that the set of initial positions that lead to the same location form a curve. We extract these curves by devising a derived vector field in which they appear as tangent curves. Most importantly, the derived vector field only involves forward integrated flow map gradients, which are much more stable to compute than backward trajectories. After extraction, we interactively visualize the curves in the domain and display the reached velocities using glyphs. In addition, we encode the rate of change of the terminal velocity along the curves, which gives a notion for the convergence to the terminal velocity. With this, we present the first solution to the source inversion problem that considers actual inertial trajectories. We apply the method to steady and unsteady flows in both 2D and 3D domains.en_US
dc.description.number3en_US
dc.description.sectionheadersFlow Visualizationen_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume35en_US
dc.identifier.doi10.1111/cgf.12913en_US
dc.identifier.issn1467-8659en_US
dc.identifier.pages371-380en_US
dc.identifier.urihttps://doi.org/10.1111/cgf.12913en_US
dc.identifier.urihttps://diglib.eg.org:443/handle/10
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectI.3.3 [Computer Graphics]en_US
dc.subjectPicture/Image Generationen_US
dc.subjectLine and curve generationen_US
dc.titleSource Inversion by Forward Integration in Inertial Flowsen_US
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35-Issue 3
EuroVis16: Eurographics Conference on Visualization