Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
QUADTREE IMPLEMENTATION FOR H-ADAPTIVE MESH REFINEMENT: A CASE STUDY IN MULTI-DOMAIN PROBLEMS
Submission Author:
Gabriel Nunes , SP , Brazil
Co-Authors:
Gabriel Nunes, Elisan dos Santos Magalhães, Guilherme Borges Ribeiro
Presenter: Gabriel Nunes
doi://10.26678/ABCM.COBEM2023.COB2023-2081
Abstract
This study presents an implementation of a quadtree-based, h-adaptive algorithm for solving 2D thermal conduction problems involving multiple materials. The algorithm employs Python and the Finite Volume Method (FVM) to dynamically refine and coarsen the computational mesh, improving the efficiency and accuracy of the solution. This approach addresses the challenges associated with computational cost and localization of features in material interface problems. The quadtree structure is used to efficiently manage the hierarchical subdivisions of the domain, allowing for a high degree of local refinement where needed, such as at material interfaces, while keeping coarser grids elsewhere. The quadtree structure is navigated via cardinal direction-based functions to identify neighboring elements and allow for the application of boundary conditions. In this work, we benchmark our algorithm against analytic solutions for one-dimensional problems and observe improved error convergence with increased levels of refinement. For the two-dimensional problem, we propose a setup involving a plate with two subdomains and provide a detailed procedure to analyze the resulting temperature field which obtained solution was successfully validated using a commercial software. Refined meshes outperformed base-level uniform meshes in aligning with asymptotic values. The computational demand of the solver is predominantly driven by element count and represents the most significant effort when compared to the preceding data structuring operations. However, the study provides insights into the restructuring of the quadtree, indicating that this operation might become a bottleneck in inherently transient problems. Overall, integrating mesh adaption with quadtrees delivers a robust solution, underscoring its potential for advanced research in transport phenomena.
Keywords
Adaptive mesh refinement, quadtree, multi-domain, heat conduction
