Mesh Quality Agglomeration algorithm for the Virtual Element Method applied to Discrete Fracture Networks

TL;DR

This paper introduces a geometry-based mesh simplification algorithm for the Virtual Element Method, significantly reducing computational complexity in modeling complex fracture networks.

Contribution

It presents a novel quality-based agglomeration algorithm that simplifies polygonal meshes in Discrete Fracture Networks using geometric properties, enhancing efficiency.

Findings

Reduces degrees of freedom in mesh-based simulations.

Demonstrates robustness across various fracture network configurations.

Maintains accuracy while simplifying complex geometries.

Abstract

We propose a quality-based optimization strategy to reduce the total number of degrees of freedom associated to 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 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.