A multidimensional positive definite remapping algorithm for unstructured meshes

We report on developments of a second-order, conservative, sign-preserving remapping scheme for Arbitrary Lagrangian-Eulerian (ALE) methods operating on unstructured meshes. The remapping uses concepts of the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA).

The non-oscillatory infinite gauge option of MPDATA remapping is derived in volume coordinates and is based upon a general and compact edge-based data structure, developed for use within an arbitrary finite volume framework. A Flux Corrected Transport style of limiting ensures monotonicity preservation, while the construction of volume coordinates utilises median dual polygonal finite volume cells.

Theoretical developments are supported by numerical testing involving idealised cases with prescribed mesh movement for advection of scalars. The numerical investigations include an asymptotic mesh convergence study and comparisons with both MPDATA and Van Leer MUSCL remapping schemes operating on Cartesian meshes. The results demonstrate that the proposed scheme is suitable for providing accurate ALE remapping for unstructured meshes.