Department of Mathematics
Highly Parallel Algorithms for Fluid-Structure Interaction Problems and Applications
This is a Research Grants Council (RGC)/ National Natural Science Foundation of China (NSFC) joint research grants to support collaborative research between HKUST and Shenzhen Institute of Advanced Technology on blood fluid simulations with HK$1.17M from RGC and RMB 1M from NSFC.
Fluid-structure interaction (FSI) problems where one or more elastic or solid structures interact with an internal or surrounding fluid flow, play prominent roles in many scientific and engineering fields. Application of fluid-structure interaction (FSI) methods in simulation-based medical planning is particularly demanding nowadays. Artery disease is closely associated with flow properties of the blood and with the interaction between the blood and the vessel wall. In particular, areas of turbulence, flow recirculation, or places where the artery wall is subject to low or oscillating shear stress are at higher risk for plaque formation and disease. Accurate modeling of these flow characteristics might enable better prediction of when and where artery disease will occur and lead to more accurate, less invasive, and more timely treatment.
In this project, trustworthy model in presenting both the fluid (blood) and structure (vessel) properly is investigated, by comparing between Newtonian and non-Newtonian model of fluid, linear and non-linear elastic model of structure and various inlet/outlet boundary conditions. To solve the fully coupled system for the use of realistic applications requires the development of solution algorithms that are both computationally efficient and suitable for high performance parallel computers with a large number of processors. A class of Newton-Krylov (NK) methods is developed with an overlapping restricted additive Schwarz preconditioner for solving the nonlinear systems arising from the fully coupled FSI problems, with emphasis on the robustness and the parallel scalability. Moreover, some advanced mass conservative discretization techniques, numerical interface coupling approaches and adaptive refinement methods are also developed.
Related research publications:
- Zhang, Xing ; Luo, Li; Wang, Xiaoping; A Numerical Study of Fluid-Particle Interaction with Slip Boundary Condition; NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS. , v. 11, (4), November 2018, p. 795-809
- Du, Jie; Chung, Eric T.; Lam, Ming Fai; Wang, Xiaoping; Discontinuous Galerkin Method with Staggered Hybridization for a Class of Nonlinear Stokes Equation; Journal of Scientific Computing. , v. 76, (3), September 2018, p. 1547-1577
- L. Luo, X-P Wang, and X-C Cai, An efficient finite element method for simulation of droplet spreading on a topologically rough surface, Journal of Computational Physics, Vol 349 (2017), 233-252
- Li Luo, Qian Zhang, Xiao-Ping Wang, Xiao-Chuan Cai, A parallel finite element method for 3D two-phase moving contact line problems in complex domains, Journal of Scientific Computing, 72 (2017), 1119-1145
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- Chair Professor, Department of Mathematics