【数学学院】Numerical Studies for Unsteady Moving Interface Problems and Applications to Fluid-Structure Interactions (FSI)

报告题目: Numerical Studies for Unsteady Moving Interface Problems and Applications to Fluid-Structure Interactions (FSI)

报告人：孙澎涛 教授

单位：Department of Mathematical Sciences, University of Nevada, Las Vegas

时间：2018年6月27日（周三）下午4:30-5:30

地点：数学学院东409报告厅

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.

来源链接：http://math.scu.edu.cn/info/1062/3232.htm