一、题目

Simulating Fluids with Irregular and Moving Boundaries

二、主讲人

张庆海

三、摘要

When simulating fluids with moving boundaries, current methods avoid geometry and topology by converting them into numerically solving PDEs. To remove limitations of this approach, we tackle geometric and topological problems with tools in geometry and topology. First, we propose a topological space, called the Yin space, as a mathematical model of physically meaningful regions. Second, we equip the Yin space, both theoretically and algorithmically, with a Boolean algebra for fluids of arbitrarily complex topology. Third, we develop the MARS framework to unify current interface tracking methods, to analyze their accuracy and stability, and to foster fourth- and higher-order methods of interface tracking and curvature estimation. Traditional finite difference and finite volume methods have long been criticized for their inadequacy of dealing with irregular geometries. This weakness can be very much alleviated by MARS. We demonstrate this point by a fourth-order projection method for numerically solving the incompressible Navier-Stokes equations with structured rectangular grids on irregular domains.

四、主讲人简介

张庆海，本科和硕士均毕业于清华大学，在美国康奈尔大学获得博士学位。曾在美国劳伦斯伯克利国家实验室和犹他大学做博士后，现为浙江大学数学学院教授。主要研究领域是动边界流体的高保真算法，也应用计算的手段探究了一些多相流问题；在SIAM Review, PNAS, MathComp, SINUM, SISC, CMAME, JCP等知名期刊上发表论文20多篇。

五、邀请人

杜宁

六、时间

11月20日（周五）16:00-17:00

七、地点

腾讯会议，会议ID：108 511 552

八、主办方

山东大学数学学院