Convex Polygon Packing Based Meshing Algorithm for Modeling of Rock and Porous Media

Abstract

In this work, we propose new packing algorithm designed for the generation of polygon meshes to be used for modeling of rock and porous media based on the virtual element method. The packing problem to be solved corresponds to a two-dimensional packing of convex-shape polygons and is based on the locus operation used for the advancing front approach. Additionally, for the sake of simplicity, we decided to restrain the polygon rotation in the packing process. Three heuristics are presented to simplify the packing problem: density heuristic, gravity heuristic and the multi-layer packing. The decision made by those three heuristic are prioritizing on minimizing the area, inserting polygons on the minimum Y coordinate and pack polygons in multiple layers dividing the input in multiple lists, respectively. Finally, we illustrate the potential of the generated meshes by solving a diffusion problem, where the discretized domain consisted in polygons and spaces with different conductivities. Due to the arbitrary shape of polygons and spaces that are generated by the packing algorithm, the virtual element method was used to solve the diffusion problem numerically.