Piecewise linear volume tracking in spherical coordinates

We present a detailed description of a geometric piecewise linear (PLIC) volume tracking algorithm for spherical coordinates, which is a component of a flow solver being developed to study contact line dynamics on small particles. Tests demonstrate the robustness of the method, and include reconstructions of various geometries, and tests of the split advection algorithm. Reconstruction is shown to be first-order accurate; errors associated with the advection algorithm decrease at a rate greater than first-order. Finally, the paper demonstrates the implementation of a contact angle model.