WLS-ENO remap: Superconvergent and non-oscillatory weighted least squares data transfer on surfaces

Abstract

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 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 (2016) [58], WLS-ENOR adapts WLS-ENO to remap by enhancing it to resolve not only the severe oscillations due to C0 discontinuities, but also the accumulated effect of mild oscillations due to C1 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, delivering higher than (p+1)st-order convergence with even-degree p. We compare WLS-ENOR with some commonly used methods, including consistent interpolation, L2 projection, moving least squares, and radial basis functions. We show that WLS-ENOR has high accuracy and low dissipation in smooth regions, and is non-oscillatory and minimally diffusive near discontinuities.