Mesh quality agglomeration algorithm for the virtual element method applied to discrete fracture networks

Abstract

We propose a quality-based optimization strategy to reduce the total number of degrees of freedom associated with a discrete problem defined over a polygonal tessellation with the Virtual Element Method. The presented Quality Agglomeration algorithm relies only on the geometrical properties of the problem polygonal mesh, agglomerating groups of neighboring elements. We test this approach in the context of fractured porous media, in which the generation of a global conforming mesh on a Discrete Fracture Network leads to a considerable number of unknowns, due to the presence of highly complex geometries (e.g. thin triangles, large angles, small edges) and the significant size of the computational domains. We show the efficiency and the robustness of our approach, applied independently on each fracture for different network configurations, exploiting the flexibility of the Virtual Element Method in handling general polygonal elements.

A Survey of Indicators for Mesh Quality Assessment

“…Further agglomerations are possible, in particular, far from the fracture constraints. Recently, an agglomeration approach driven by the quality indicator (30) has been proposed in [SVB*22]. Extensions to whole three‐dimensional domains are currently under study, with preliminary results in [BGS22].…”