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Summary A typical Arbitrary Lagrangian-Eulerian (ALE) 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, which 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. This article is protected by copyright. All rights reserved.

Remapping is one of the essential parts of most arbitrary Lagrangian-Eulerian methods. Here, we extend the idea of swept integration introduced in (J. Comput. Phys. 2003; 184(1):266-298) to meshes with connectivity changing in Voronoi-like manner. To demonstrate properties of the developed method, we present several numerical examples.