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