Efficient Generation of Unstructured Control Volumes in 2D and 3D

Title: Efficient Generation of Unstructured Control Volumes in 2D and 3D

Abstract: This research article proposes an algorithm for generating unstructured cell-centered control volumes, which are useful for the control volume method in two and three-dimensional spaces. The algorithm is designed to work with randomly located points in a domain and its boundary, ensuring that edges of some polygons (in 2D) or tetrahedrons (in 3D) are perpendicular to lines connecting two points. This method improves upon existing techniques by reducing storage requirements and making it easier to handle adaptability in time and complex geometries.

Main Research Question: How can we generate unstructured cell-centered control volumes for the control volume method in 2D and 3D, while ensuring that edges are perpendicular to connecting lines and reducing storage requirements?

Methodology: The algorithm begins by generating circles with unknown radii around randomly located points in the domain. It then solves a system of equations to find the point where these circles intersect, ensuring that edges are perpendicular to connecting lines. This process is repeated for each point, creating a mesh of non-overlapping control volumes.

Results: The research shows that the proposed algorithm successfully generates unstructured cell-centered control volumes in 2D and 3D, with edges perpendicular to connecting lines and minimal storage requirements. The algorithm's efficiency and accuracy were tested and confirmed through various simulations and examples.

Implications: The efficient generation of unstructured control volumes in 2D and 3D has significant implications for various fields, including engineering, chemistry, and physics. The proposed algorithm can be applied to complex geometries, making it easier to represent solutions and solve problems requiring unstructured meshes. Additionally, the algorithm's ability to handle adaptability in time and its minimal storage requirements make it an attractive solution for large-scale simulations and applications.

Link to Article: https://arxiv.org/abs/0202038v1 Authors: arXiv ID: 0202038v1