学术报告

题      目：Numerical PDEs for Fluid-Structure Interaction (FSI) Problems

报  告  人：孙澎涛   教授  (邀请人：钟柳强 )

                                    美国内华达大学

时      间：6月2日  11：00-12：00

地     点：数科院西楼112教室

报告人简介:

       孙澎涛博士，现任美国内华达大学拉斯维加斯分校(University of Nevada Las Vegas, UNLV) 数学系的终身正教授，博士生导师。1997 年在中国科学院数学研究所获博士学位。在 2007 年入 职美国内华达大学(UNLV)之前，曾先后在中国科学院、香港理工大学、美国宾夕法尼亚州立 大学、加拿大西蒙弗雷泽大学担任博士后、副研究员、助理教授等职位。主要研究方向:偏微分 方程数值解，有限元/有限体积方法的数值分析，自适应有限元方法，区域分解方法，相场方法， 以及对流体动力学、固体力学、流─固耦合动力学、燃料电池动力学、血液动力学、电流体动力 学等多物理场问题的建模、科学与工程计算的算法、分析、实现等研究。在著名的科学期刊上发 表学术论文 100 余篇。2008 年以来的研究课题连续被美国国家科学基金会(NSF)，西蒙斯基金 会(Simons Foundation)和内华达大学的教授研究奖励基金所资助。于 2016 年获得内华达大学理 学院颁发的杰出研究奖。

摘      要：

       The interaction of a flexible structure with a flowing fluid in which it is submersed or by which it is surrounded gives rise to a rich variety of physical phenomena with applications in many fields of engineering, named as fluid-structure interactions (FSI). To understand these phenomena, we need to find an effective way to model and simulate both fluid and structure, simultaneously, by investigating the interaction between them. In general, FSI problems require the fluid and the structure fields at the common interface to share not only the same velocity but also the common traction force. There are currently several major approaches classified with respect to the numerical treatment how the interfacie conditions of FSI are dealt with on the moving interface. In my talk, I will introduce three numerical techniques studied in my research for solving FSI problems: (1) body fitted mesh (arbitrary Lagrangian-Eulerian) method, (2) body-unfitted mesh (fictitious domain) method, and (3) meshfree (deep neural network) method. 

      Our applications to FSI problems range from hydrodynamics (physics) to hemodynamics (biology, physiology), in which the involved structures are either incompressible or compressible and bear a deformable and/or rotational constitutive relation while the surrounding fluid flow is incompressible or nearly incompressible. In particular, our well-developed numerical methods have been successfully applied to several realistic dynamic FSI problems. Some belong to the hydrodynamics that involve a deforming and/or spinning turbine which is immersed in the fluid flow. Others belong to the hemodynamical applications, e.g., a rotating artificial heart pump inside the artery to help on curing the heart−failure patients, and an intravascular stent inside the blood fluid to treat the aneurismal patients. Both applications are to improve the human cardiovascular system and to remedy cardiovascular diseases. Some animations will be shown in this talk to illustrate that the proposed and well analyzed numerical methods can produce high fidelity numerical results for realistic FSI problems in an efficient and accurate fashion.