Divergence Preserving Approximation of Vector Fields

Fluids are often simulated on regular grids. At each grid point, the fluid velocity is stored as a vector. In order to analyze the flow, most flow-visualization algorithms interpolate the vector field at non-grid points in a component-wise fashion. This straightforward approach is not conservative i.e., the interpolated vector-field is no longer divergence-free.

The aim of this research project is two fold:

1) Quantify the error introduced due to this component-wise treatment.

2) Investigate efficient strategies that attempt to lower the error with little or no overhead. Such strategies include: using alternate sampling lattices, prefiltering the vector data so as to minimize the divergence, and using alternate flow-field representations that are inherently divergence-free.

Faculty Supervisor:

Usman Alim

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University:

University of Calgary

Program:

Globalink Research Internship