Modeling and Simulations of FluidStructure Interactions FSI FSI

Modeling and Simulations of Fluid-Structure Interactions (FSI) FSI Community in Dr. Jinchao Xu’s Group (in alphabetic order): Gong, Shihua Leng, Wei Sun, Pengtao Wang, Lu (Ph. D Stud, PKU) (Res Asst, CAS) (Assoc Prof, UNLV) (Postdoc, LLNL) Yang, Kai Xu, Jinchao Zhang, Chensong Zhang, Lixiang (Postdoc, Stanford) (Prof, PSU) (Res Assoc, CAS) (Prof, KMUST)

FSI Modeling • Fluid motion: • Structure motion: • Interface conditions: • ALE mapping:

Monolithic FSI Simulation • Rotational linear elasticity equation (Yang, Sun, Wang, Xu & Zhang 2016) : where, R is the rotational matrix. • Monolithic weak form of fluid-rotating structure interactions:

Monolithic FSI Solver • Key contributions (Xu & Yang 2015): Ø Well-posedness of discretized linear systems Ø Optimal block preconditioners • Block lower triangular preconditioners: Fluid & structure velocity block Fluid pressure mass matrix Fluid pressure block

Fluid-Rotating Structure Interactions • Key contributions (Yang, Sun, Wang, Xu & Zhang 2016): Ø Linearized elasticity in rotated configuration Ø A new ALE method designed for rotating structure • Rotating fluid buffer zone • Locally shifting boundary nodes of buffer zone & stationary fluid domain

FSI Applications • Example 1: 3 D simulation of a propeller/turbine (Sun, Wang & Yang 2014)

FSI Applications • Example 2: Artificial heart pump (Sun & Leng 2015)

FSI Applications • Example 3: Cardiovascular aorta, aneurism & stent (Gong & Wang 2014 -16)

Parallel computing of FSI • Parallel rotating partition: • Parallel heart pump FSI:

Parallel computing of FSI • Parallel solver • Monolithic approach: Newton-Krylov method with overlapping ASM preconditioner (X. Cai et al 2010 -14) • Blockwise preconditioner (A. Quarteroni et al 2011 -14) • Multiplicative preconditioner: blockwise preconditioner X ASM • Parallel computing setup on Tian. He 2 Ø# Verts: 1. 2 M; # Elems: 6. 9 M; # DOFs: 8. 7 M Ø 4000 cores ØTime step size: 5 x 10 e-5 • Parallel computing time ØEach time step (Newton’s iterations, fixed-point iterations) costs about 20 s ØEntire simulation costs about 1 day to reach t=0. 1

Acknowledgement • P. Sun, L. Wang, J. Xu, K. Yang & Zhang were supported by Yunnan Provincial Science and Technology Department Research Award: Interdisciplinary Research in Computational Mathematics and Mechanics with Applications in Energy Engineering. • J. Xu, L. Wang, and K. Yang were supported by the U. S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research as part of the Collaboratory on Mathematics for Mesoscopic Modelingof Materials (Contract No. DE-SC 0009249 and DE-SC 0014400). • J. Xu, L. Wang, and K. Yang were supported by National Natural Science Foundation of China (NSFC) (Grant No. 91430215). • P. Sun was supported by NSF Grant DMS-1418806. • L. Zhang was supported by the NSFC (Grant No. 51279071) and the Doctoral Foundation of the Ministry of Education of China (Grant No. 20135314130002).