Scalable adaptive PDE solvers in arbitrary domains

• Published in: arXiv.org 2021-08
• Main Authors: Kumar, Saurabh, Ishii, Masado, Milinda Fernando, Gao, Boshun, Tan, Kendrick, Ming-Chen, Hsu, Krishnamurthy, Adarsh, Sundar, Hari, Baskar Ganapathysubramanian
• Format: Article
• Language: English
• Subjects: Computational fluid dynamics; Differential geometry; Domains; Drag coefficients; Finite element method; Fluid flow; Octrees; Partial differential equations; Reynolds number
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2108.03757

Efficiently and accurately simulating partial differential equations (PDEs) in and around arbitrarily defined geometries, especially with high levels of adaptivity, has significant implications for different application domains. A key bottleneck in the above process is the fast construction of a `good' adaptively-refined mesh. In this work, we present an efficient novel octree-based adaptive discretization approach capable of carving out arbitrarily shaped void regions from the parent domain: an essential requirement for fluid simulations around complex objects. Carving out objects produces an \(\textit{incomplete}\) octree. We develop efficient top-down and bottom-up traversal methods to perform finite element computations on \(\textit{incomplete}\) octrees. We validate the framework by (a) showing appropriate convergence analysis and (b) computing the drag coefficient for flow past a sphere for a wide range of Reynolds numbers (\(\mathcal{O}(1-10^6)\)) encompassing the drag crisis regime. Finally, we deploy the framework on a realistic geometry on a current project to evaluate COVID-19 transmission risk in classrooms.