Cell agglomeration strategy for cut cells in eXtended discontinuous Galerkin methods

Abstract: In this work, a cell agglomeration strategy for the cut cells arising in the extended discontinuous Galerkin (XDG) method is presented. Cut cells are a fundamental aspect of unfitted mesh approaches where complex geometries or interfaces separating sub-domains are embedded into Cartesian background grids to facilitate the mesh generation process. In such methods, arbitrary small cells occur due to the intersections of background cells with embedded geometries and lead to discretization difficulties due to their diminutive sizes. Furthermore, temporal evolutions of these geometries may lead to topological changes across different time steps. Both of these issues, i.e., small-cut cells and topological changes, can be addressed with a cell agglomeration technique. In this work, a comprehensive strategy for the typical issues associated with cell agglomeration in three-dimensional and multiprocessor simulations is provided. The proposed strategy is implemented into the open-source software package BoSSS and tested with 2- and 3-dimensional simulations of immersed boundary flows.