# Qinghai Zhang: Fluid Modeling in Three Dimensions: Topological Classification, Boolean Algebra, Geometric Representation, and Their Applications to Interface Tracking and Mean Curvature Flows

**Time: **
Thu 2022-11-17 14.00 - 15.00

**Location: **
Zoom

**Video link: **
Meeting ID: 632 9929 3349

**Participating: **
Qinghai Zhang (Zhejiang University)

**Abstract: **

Solid modeling has been an established field while fluid modeling is still an undefined concept. However, there is a need of fluid modeling in numerically solving PDEs on complex moving domains: sometimes we have to have a solid ground for the topology and geometry of complex domains so that subsequent analysis can be performed. We answer this need by proposing for three-dimensional continua a modeling space, a complete topological classification, a Boolean algebra, and a geometric representation of their boundary. We united these techniques in a framework for numerically solving geometric PDEs such as the mean curvature flows with fourth- and higher-order convergence.