A multi-resolution interpolation scheme for pathline based Lagrangian flow representations

@inproceedings{Agranovsky2015AMI,
  title={A multi-resolution interpolation scheme for pathline based Lagrangian flow representations},
  author={Alexy Agranovsky and Harald Obermaier and Christoph Garth and Kenneth I. Joy},
  booktitle={Electronic Imaging},
  year={2015}
}
Where the computation of particle trajectories in classic vector field representations includes computationally involved numerical integration, a Lagrangian representation in the form of a flow map opens up new alternative ways of trajectory extraction through interpolation. In our paper, we present a novel re-organization of the Lagrangian representation by sub-sampling a pre-computed set of trajectories into multiple levels of resolution, maintaining a bound over the amount of memory mapped… 
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10 Citations
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10 Citations

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TLDR
A formal analysis of the theoretical bound on the error when advecting pathlines using this method is presented and it is found that for interpolation-based pathline tracing the error is closely related to the divergence in the flow field.
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TLDR
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TLDR
The rendering process is accelerated significantly, which allows us to compute video sequence of high-resolution FTLE animations in a much more reasonable time frame and follows two orthogonal approaches to improve on the rendering process: the volumetric light path integration in gradient domain and an acceleration of the transmittance estimation.
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TLDR
Experimental results show that the proposed flux-based stream functions for generating streamlines in parallel offers higher streamline computation performance with higher scalability than traditional particle-tracing based method.
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TLDR
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Analysis Enhanced Particle-based Flow Visualization
TLDR
A number of flow analysis techniques and their extension for PFS data analysis are studied, including the FTLE approach, Jacobian analysis, and an attribute accumlation framework, and it is demonstrated that these analyses can reveal some interesting underlying flow patterns that would be hard to see otherwise via a number of PFS simulated flows.
Backward Finite-Time Lyapunov Exponents in Inertial Flows
TLDR
It is shown that FTLE on the influence curve vector field is in agreement with preferential particle settling and more importantly it is not only valid for small (near-tracer) particles, which enables backward integration with more general equations of motion in unsteady spatio-velocity phase spaces.
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TLDR
This paper constructs a large fluid flow data set and applies it to a deep learning problem in scientific visualization, improving the accuracy of flow map interpolations, allowing a more precise flow analysis at a reduced memory IO footprint.

References

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