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

2. FSI Modeling ALE mapping: Fluid motion: Structure motion:
Interface conditions:
ALE mapping:

3. 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:

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

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

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

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

8. FSI Applications
Example 3: Cardiovascular aorta, aneurism & stent (Gong & Wang )

9. Parallel computing of FSI
Parallel rotating partition:
Parallel heart pump FSI:

10. Parallel computing of FSI
Parallel solver
Monolithic approach: Newton-Krylov method with overlapping ASM preconditioner (X. Cai et al )
Blockwise preconditioner (A. Quarteroni et al )
Multiplicative preconditioner: blockwise preconditioner X
ASM
Parallel computing setup on TianHe2
# Verts: 1.2M; # Elems: 6.9M; # DOFs: 8.7M
4000 cores
Time step size: 5x 10e-5
Parallel computing time
Each time step (Newton’s iterations, fixed-point iterations) costs about 20s
Entire simulation costs about 1 day to reach t=0.1

11. 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 and DE-SC ).
J. Xu, L. Wang, and K. Yang were supported by National Natural Science Foundation of China (NSFC) (Grant No ).
P. Sun was supported by NSF Grant DMS
L. Zhang was supported by the NSFC (Grant No ) and the Doctoral Foundation of the Ministry of Education of China (Grant No ).