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 subdomains are embedded into structured 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, that is, small-cut cells and topological changes, can be addressed with a cell agglomeration technique, independent of discretization. However, cell agglomeration encounters significant difficulties in three dimensions due to the complexity of neighborship and issues like cycles and parallel agglomeration chains. The proposed strategy introduces a robust framework that mitigates these problems by incorporating methods for cycle prevention, chain agglomeration, and parallelization. Implemented in the open-source software package BoSSS, this strategy has been successfully tested on multiprocessor systems using dynamic multiphase test cases in both two and three dimensions, enabling simulations that were previously infeasible.