Creating analytically divergence-free velocity fields from grid-based data

Bharath Ravu

doi:10.1016/j.jcp.2016.07.018

Creating analytically divergence-free velocity fields from grid-based data

2016-10-01

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DOI：10.1016/j.jcp.2016.07.018

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We present a method, based on B-splines, to calculate a C(2)continuous analytic vector potential from discrete 3D velocity data on a regular grid. A continuous analytically divergence-free velocity field can then be obtained from the curl of the potential. This field can be used to robustly and accurately integrate particle trajectories in incompressible flow fields. Based on the method of Finn and Chacon (2005) [10] this new method ensures that the analytic velocity field matches the grid values almost everywhere, with errors that are two to four orders of magnitude lower than those of existing methods. We demonstrate its application to three different problems (each in a different coordinate system) and provide details of the specifics required in each case. We show how the additional accuracy of the method results in qualitatively and quantitatively superior trajectories that results in more accurate identification of Lagrangian coherent structures. (C) 2016 Elsevier Inc. All rights reserved.

Keywords:

Divergence-free interpolation

Discrete velocity data

Vector potential

Lagrangian coherent structures

Creating analytically divergence-free velocity fields from grid-based data

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