题目：Numerical Studies for Unsteady Moving Interface Problems and Applications to Fluid-Structure Interactions
报告人：Prof. Pengtao Sun （美国内华达大学拉斯维加斯分校）
摘要：In this talk, I will present our recent numerical methodology studies for unsteady moving interface problems and applications to dynamic fluid-structure interaction (FSI) problems. Our numerical methodologies include the arbitrary Lagrangian−Eulerian (ALE) method, the distributed Lagrange multiplier/fictitious domain (DLM/FD) method and their combinations with the mixed finite element method. A fully coupled (monolithic) mixed finite element approximation is developed for all numerical methodologies to unconditionally stabilize numerical computations for moving- interface and FSI problems. Numerical analyses on the well-posedness, stability and convergence are carried out for the proposed monolithic ALE and DLM/FD methods when they are applied to various moving−interface problems. Convergence theorems conclude those numerical analyses with an optimal convergence in regard to the regularity assumption of real solutions. All theoretical results are validated by numerical experiments as well.
Our applications to FSI problems range from hydrodynamics to hemodynamics, in which the involved structure is either incompressible or compressible and bears a deformable and/or rotational constitutive relation while the surrounding fluid flow is incompressible or nearly incompressible. In particular, our well developed ALE method has 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., an artificial heart pump is rotating inside the artery to cure the heart−failure patients, and an intravascular stent is installed inside the artery by interacting with the blood flow as well as the artery to cure 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.
Dr. Pengtao Sun is the Full Professor of Department of Mathematical Sciences in University of Nevada, Las Vegas (USA). Dr. Sun obtained his PhD degree from Institute of Mathematics, Chinese Academy of Sciences in 1997, and his Master’s and Bachelor degree from Shandong University (China) in 1994 and 1991, respectively. Before joining University of Nevada, Las Vegas in 2007, he worked as Postdoctoral Fellow, Research Associate and Assistant Professor in Chinese Academy of Sciences, Hong Kong Polytechnic University, Pennsylvania State University (USA) and Simon Fraser University (Canada). Dr Sun’s primary research fields are Numerical Solutions of Partial Differential Equations, Numerical Analysis on Finite Element/Finite Volume Methods, Adaptive Finite Element Method, and Scientific and Engineering Computing with applications to miscellaneous multiphysics problems in the field of solid mechanics, fluid dynamics, fuel cell dynamics, fluid-structure interactions in hydrodynamics and hemodynamics, electrohydrodynamics, and etc. Dr. Sun’s research has been continuously supported by National Science Foundation (DMS-0913757, 1418806) and Faculty Opportunity Awards (UNLV) since 2008.
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