Combined swept region and intersection‐based single‐material remapping method. (8th May 2017)

• Record Type: Journal Article
• Authors: Klima, Matej; Kucharik, Milan; Shashkov, Mikhail
• Is Part Of: International journal for numerical methods in fluids. Volume 85:Number 6(2017)
• Page Start: 363
• Page End: 382
• Publication Date: 2017-05-08
• Subjects: ALE – arbitrary Lagrangian–Eulerian -- compressible flow -- error estimation -- polygon intersections -- remapping -- swept regions; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4384
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: A typical arbitrary Lagrangian–Eulerian algorithm consists of a Lagrangian step, where the computational mesh moves with the fluid flow; a rezoning step, where the computational mesh is smoothed and repaired in case it gets too distorted; and a remapping step, where all fluid quantities are conservatively interpolated on this new mesh. In single‐material simulations, the remapping process can be represented in a flux form, with fluxes approximated by integrating a reconstructed function over intersections of neighboring computational cells on the original and rezoned computational mesh. This algorithm is complex and computationally demanding – Therefore, a simpler approach that utilizes regions swept by the cell edges during rezoning is often used in practice. However, it has been observed that such simplification can lead to distortion of the solution symmetry, especially when the mesh movement is not bound by such symmetry. For this reason, we propose an algorithm combining both approaches in a similar way that was proposed for multi‐material remapping (two‐step hybrid remap). Intersections and exact integration are employed only in certain parts of the computational mesh, marked by a switching function – Various different criteria are presented in this paper. The swept‐based method is used elsewhere in areas that are not marked. This way, our algorithm can retain the beneficial symmetry‐preserving capabilities of intersection‐based remapping while keeping the overall computational cost moderate. Abstract : We propose a new remapping algorithm within the context of ALE methods. It combines the swept‐based and intersection‐based approaches in different parts of the domain. The more expensive intersections are employed only in cells marked by a switching function – Various criteria are presented in the paper. The swept‐based method is used elsewhere. The aim of our algorithm is to keep the beneficial symmetry‐preserving capabilities of the intersection‐based method at a lower computational cost.