Adaptive partition of unity interpolation method with moving patches

The adaptive partition of unity interpolation method, introduced by Aiton and Driscoll, using Chebyshev local interpolants, is explored for interpolating functions with sharp gradients representing two-medium problems. For that evolve under vector fields, the patches (covers) can be shifted resized to follow changing dynamics profiles. method tested selected 1D 2D problems linear divergence-free fields. In those cases, volume fraction in each patch contributing conservation throughout domain kept high accuracy down machine precisions. Applications could benefit from include tracking multiphase flow modeling.