Professor Pengtao Sun,Department of Mathematical Sciences, University of Nevada

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[1]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.