## F2F/Virtual Tea & Colloquium with Hari Sundar

"Scalable adaptive PDE solvers in arbitrary domains"

### Oct 20, 2021 Schedule:

Tea Time - F2F ( 417 DSL) / Virtual ( Zoom)

03:00 to 03:30 PM Eastern Time (US and Canada)

Colloquium - F2F ( 499 DSL) / Virtual ( Zoom)

03:30 to 04:30 PM Eastern Time (US and Canada)

Meeting # 942 7359 5552

## Abstract:

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 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 ({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.