2 199 Navier-Stokes { u t - v 2 u + u u + 1 p = f 1 ρ u = 0 ux y Case25CTA z= { u LC6 60% T n = 0 2 CAS Case25pre ux y z= 0 Case25post u = u x u

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1 42 2 Vol 42 No Journal of Jiangxi Normal UniversityNatural Science Mar * CPU % O 246 A DOI /j cnki issn WSS WSS Y G Abdoulaev 8 1 CPU % CPU 2 3 G Abdoulaev AA01A snzma@ 126 com

2 199 Navier-Stokes { u t - v 2 u + u u + 1 p = f 1 ρ 1 2 1 u = 0 ux y Case25CTA z= { u LC6 60% T n = 0 2 CAS Case25pre ux y z= 0 Case25post u = u x u y u z u Mimics ρ μ v = μρ p t T 3 3 n f 2 2 70%

2 2 199 Navier-Stokes { u t - v 2 u + u u + 1 p = f 1 ρ u = 0 ux y Case25CTA z= { u LC6 60% T n = 0 2 CAS Case25pre ux y z= 0 Case25post u = u x u y u z u Mimics ρ μ v = μρ p t T 3 3 n f % Case25pre ICEM Newton-Krylov- SchwarzNKS 10 NKS Newton Krylov Schwarz 3 Case25pre Step 1 X 0 k = Case25post Step 2 FX Jacobian J k J k = FX k Newton-Krylov-Schwarz Step 3 Krylov M k Navier-Stokes 1~ 2 Jacobian S k P 1 -P 1 J k M k - 1 M k S k + FX k η k FX k 2 Step 4 τ k

200 2018 X k + 1 = X k + τ k S k Step 5 1 k < N R δ i jk X = X k + 1 k = k + 1 Step 2 M k Schwarz N s M AS = Ω i R δ i jk = 11 j < N i = 0 Schwarz R δ i T B -1 i R δ i η k i = 1 Step 2 B -1 i Ω δ i

3 X k + 1 = X k + τ k S k Step 5 1 k < N R δ i jk X = X k + 1 k = k + 1 Step 2 M k Schwarz N s M AS = Ω i R δ i jk = 11 j < N i = 0 Schwarz R δ i T B -1 i R δ i η k i = 1 Step 2 B -1 i Ω δ i 80% Jacobian J i J -1 i GMRES NKS Newton Krylov GMRES Schwarz Schwarz Krylov Krylov 3 1 Krylov 1 ρ = Krylov kg m - 3 μ = kg Schwarz Jacobian Krylov s 0 05 s Ω Ω N s 3 4 m - 1 s - 1 Ω i i = N s Case25pre Case25post Ω δ i Ω i Ω δ i Ω δ > 0 Ω δ i Ω i N N i Ω Ω δ i Ω δ i Ω R δ i R N i N WSS 01 Pa 10-2 m s -1 3 Case25pre WSS 3 4 Case25post WSS Case25pre Case25post

2 201 WSS Case25pre 1 0 49 0 64 4 Case25post WSS 1 /Pa /m s - 1 WSS /Pa FFRCFD Case25pre 6 872 6 1 98 2 86 0 49 Case25post 4 186 3 1 72 2 64 0 64 3 2 2 12 10 6 2 2 2 12 10 6 CPU 128 72 43% CPU 1 09

4 2 201 WSS Case25pre Case25post WSS 1 /Pa /m s - 1 WSS /Pa FFRCFD Case25pre Case25post CPU % CPU CPU Newton GMRES /s /%

5 J Cai Xiaochuan Gropp W D Keyes D E et al Newton-Kry- 3 lov-schwarz methods in CFD C/ /Friedrich-Karl Hebeker Notes on numerical fluid mechanics J Wiesbaden CT 3 J J 12Hwang Fengnan Cai Xiaochuan A parallel nonlinear additive Schwarz preconditioned inexact Newton algorithm for incompressible Navier-Stokes equations J Journal of 6Younis H FKaazempur-Mofrad M R Chung C et al Computational Physics Computational analysis of the effects of exercise on hemo- 13Cai Xiaochuan Sarkis M A restricted additive Schwarz dynamics in the carotid bifurcation J Annals of Biomedical Engineering Peng Hongmei Yang Dequan The boundary element analysis on Y bifurcation arterial hemodynamic characteristics J Chinese Journal of Medical Physics Abdoulaev G Cadeddu S Delussu G et al ViVathe virtual vascular project J IEEE Transactions on Information Technology in Biomedicine J 9Qiao AikeGuo XinglingWu Shigui et al Numerical study of nonlinear pulsatile flow in S-shaped curved arteries J Medical Engineering and Physics Springer Newton-Krylov-Schwarz J preconditioner for general sparse linear systems J SI- AM Journal on Scientific Computing J Panerai R B Dineen N E Brodie F G et al Spontaneous in cerebral blood flow regulationcontribution of PaCO 2 J Applied Physiology The Parallel Numerical Simulation of Some Cerebral Flow WU Bokai 1 XU Wenxin 2 YAN Zhengzheng 2 SUN Zhe 1* CHEN Rongliang 2 LIU Jia 2 1 College of Mathematics and Informatics Jiangxi Normal University Nanchang Jiangxi 2 Shenzhen Institutes of Advanced Technology Chinese Academy of Sciences Shenzhen Guangdong China China AbstractA set of high performance numerical simulation system for human hemodynamics is developed The system includes the construction of 3D artery geometry from MRI images unstructured mesh generation the discretization and solution of the fluid flow equations and the analysis of the generation of results The flow equations solver part in this paper is mainly focused on and the reliability and efficiency of the system are verified by solving a real patient case of stroke including preoperative and postoperative caseswhich is provided by Beijing Tiantan Hospital The results show that the computed values including the pressure the velocity and the wall shear stress are consistent with the clinical conclusion Regarding to the parallel performance of the method an almost linear speedup is obtained with up to 128 processor cores for a case with mesh elements and the parallel efficiency is still around 72 43% Key wordshemodynamicsfinite element methodcomputational fluid dynamicsparallel computingdomain decomposition method

[1] Nielsen [2]. Richardson [3] Baldock [4] 0.22 mm 0.32 mm Richardson Zaki. [5-6] mm [7] 1 mm. [8] [9] 5 mm 50 mm [10] [11] [12] -- 40% 50%

[1] Nielsen [2]. Richardson [3] Baldock [4] 0.22 mm 0.32 mm Richardson Zaki. [5-6] mm [7] 1 mm. [8] [9] 5 mm 50 mm [10] [11] [12] -- 40% 50% 38 2 2016 4 -- 1,2, 100190, 100083 065007 -- 0.25 mm 2.0 mm d 10 = 0.044 mm 640 3 300. Richardson--Zaki,,, O359 A doi 10.6052/1000-0879-15-230 EXPERIMENTAL STUDY OF FLUID-SOLID TWO-PHASE FLOW IN A VERTICAL