Cell agglomeration strategy for cut cells in eXtended discontinuous Galerkin methods

TL;DR

This paper introduces a cell agglomeration strategy for cut cells in the extended discontinuous Galerkin method, improving the handling of small and topologically changing cells in complex geometries within unfitted mesh approaches.

Contribution

It presents a comprehensive cell agglomeration strategy specifically designed for 3D and multiprocessor simulations in the XDG framework, implemented in open-source software.

Findings

Effective handling of small cut cells in 2D and 3D simulations.

Improved stability and accuracy in immersed boundary flow simulations.

Robustness of the method across topological changes.

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.