Skeleton and level set for channel construction and flow simulation

This paper aims to introduce a unified code for fluid flow modeling in complex channels reconstructed from imagery. Given a binary image of a cross-section or projection of planar connected channels with circular cross-sections, we wish to: (1) reconstruct a three-dimensional model of the boundary of the geometry, (2) establish boundary condition of the flow field, and (3) compute a fluid simulation based on a Cartesian grid. Our solution has the following advantages. First, we use the same mathematical tools throughout the process i.e. a level set function and a skeleton to describe the geometry. The skeleton of the geometry is essential in the imagery part to transform the 2D geometry into a 3D geometry but is also essential in the fluid flow part to construct a velocity field of reference for boundary conditions in the mechanical fluid flow model. Then, the integration of the geometry into the fluid mechanic code is simplified thanks to a Cartesian grid taking into account the geometry through the level set function. Finally, this work leads to a stand-alone code capable of simulating 3D flows in geometry reconstructed 2D images. We show its usefulness in applications to medical imagery (namely angiography) and bifluid flows in microchannels.

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