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arXiv · 1411.1369

Strain-minimising Stream Surfaces

Michael Bartoň·Jiří Kosinka·Victor M. Calo
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Abstract

We study the problem of finding strain-minimising stream surfaces in a divergence-free vector field. These surfaces are generated by motions of seed curves that propagate through the field in a strain minimising manner, i.e., they move without stretching or shrinking, preserving the length of their arbitrary arc. In general fields, such curves do not exist. However, the divergence-free constraint gives rise to these 'strain-free' curves that are locally arc-length preserving when infinitesimally propagated. Several families of strain-free curves are identified and used as initial guesses for stream surface generation. These surfaces are subsequently globally optimised to obtain the best strain-minimising stream surfaces in a given divergence-free vector field. Our algorithm was tested on benchmark datasets, proving its applicability to incompressible fluid flow simulations, where our strain-minimising stream surfaces realistically reflect the flow of a flexible univariate object.

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Michael Bartoň, Jiří Kosinka, Victor M. Calo. 2014-11-05. Strain-minimising Stream Surfaces. https://arxiv.org/abs/1411.1369

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