A Multidimensional Positive Definite Remapping Algorithm for Unstructured Meshes

• Published in: Computers & fluids 2020-03, Vol.200, p.104454, Article 104454
• Main Authors: Szmelter, Joanna, Gillard, Mike
• Format: Article
• Language: English
• Subjects: Advection; Advection remapping; ALE remapping; Algorithms; Cartesian coordinates; Conservative interpolation; Data structures; Flux corrected transport; MPDATA; Multidimensional methods; Scalars
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2020.104454

•The new MPDATA based remapping for ALE, suitable for unstructured meshes, is derived.•Novel MPDATA based remapping is developed and validated for the derived PDEs.•Numerical results show benefits of the proposed approach, especially in terms of accuracy and multidimensionality. 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.