Parallel, second-order and consistent remeshing transfer operators for evolving meshes with superconvergence property on surface and volume

This paper investigates several field transfer techniques that can be used to remap data between three-dimensional unstructured meshes, either after full remeshing of the computational domain or after mesh regularization resulting from an ALE (Arbitrary Lagrangian or Eulerian) formulation. The transfer is focused on state (or secondary) variables that are piecewise discontinuous and consequently only defined at integration points. The proposed methods are derived from recovery techniques that have initially been developed by Zienkiwicz et al. in the frame of error estimation. Obtaining a higher order interpolation with the recovered fields allows reducing the inescapable diffusion error resulting from the projection on the new mesh. Several variants of the method are investigated: (a) either based on nodal patches or on element patches, (b) by enforcing the balance equation in a weak sense or in a strong sense or not, (c) by using first or second interpolation orders. A special attention is paid to the accuracy of the transfer operators for surface values, which can play a first order role in several mechanical problems. In order to take into account the constraint due to parallel calculations, a new iterative approach is proposed. All methods are evaluated and compared on analytical tests functions, both for the ALE formulation and for full remeshings, before being applied to an actual metal forming problem. In all studied examples, in addition to improved accuracy, higher order convergence rates are observed both for volume and surface values, so providing quite accurate transfer operators for various applications.