  Data remap between non-matching meshes is a critical step in multiphysics
coupling using a partitioned approach. The data fields being transferred often
have jumps in function values or derivatives. It is important but very
challenging to avoid spurious oscillations (a.k.a. the Gibbs Phenomenon) near
discontinuities and at the same time to achieve high-order accuracy away from
discontinuities. In this work, we introduce a new approach, called WLS-ENOR, or
Weighted-Least-Squares-based Essentially Non-Oscillatory Remap, to address this
challenge. Based on the WLS-ENO reconstruction technique proposed by Liu and
Jiao (J. Comput. Phys. vol 314, pp 749--773, 2016), WLS-ENOR differs from
WLS-ENO and other WENO schemes in that it resolves not only the O(1)
oscillations due to C 0 discontinuities, but also the accumulated effect of
O(h) oscillations due to C 1 discontinuities. To this end, WLS-ENOR introduces
a robust detector of discontinuities and a new weighting scheme for WLS-ENO
near discontinuities. We also optimize the weights at smooth regions to achieve
superconvergence. As a result, WLS-ENOR is more than fifth-order accurate and
highly conservative in smooth regions, while being non-oscillatory and
minimally diffusive near discontinuities. We also compare WLS-ENOR with some
commonly used methods based on L 2 projection, moving least squares, and radial
basis functions.
