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

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.