42 2 Vol 42 No 2 2018 3 Journal of Jiangxi Normal UniversityNatural Science Mar 2018 1000-5862201802-0199-05 1 2 2 1* 2 2 1 3300222 518055 1 2 12 10 6 CPU 128 72 43% O 246 A DOI10 16357 /j cnki issn1000-5862 2018 02 14 0 3 WSS 3 1 1 20 WSS 80 1-6 7 Y 2 12 10 6 2 G Abdoulaev 8 1 CPU 128 72 43% 9 7 128 CPU 2 3 G Abdoulaev 8 3 1 9 2017-11-15 863 2015AA01A302 91330111 11401564 61531166003 1983- E-mailsnzma@ 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% 1 2 2 Case25pre ICEM Newton-Krylov- SchwarzNKS 10 NKS Newton Krylov Schwarz 3 Case25pre 1 491 002 Step 1 X 0 k = 0 264 218 Case25post 1 660 071 Step 2 FX Jacobian J k J k = FX k 293 787 2 2 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 80% Jacobian J i J -1 i GMRES NKS Newton Krylov GMRES Schwarz 3 2 3 Schwarz Krylov Krylov 3 1 Krylov 1 ρ = Krylov 11-12 1 06 10 3 kg m - 3 μ = 3 5 10-3 kg Schwarz Jacobian 13-14 Krylov 15 1 25 s 0 05 s Ω Ω N s 3 4 m - 1 s - 1 Ω i i = 1 2 3 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 10 6 2 CPU Newton GMRES /s /% 1 09 10 6 2 12 10 6 4 16 5 2 324 7 6 281 1 00 1 100 00 32 5 2 329 8 3 254 2 02 2 102 42 64 5 3 353 6 1 982 3 35 4 83 63 128 5 3 450 3 1 317 4 53 8 56 67 16 5 8 261 5 10 500 1 00 1 100 00 32 5 9 290 0 5 126 2 05 2 102 42 64 5 9 335 2 3 146 3 34 4 83 44 128 5 9 381 6 1 812 5 79 8 72 43 1 1 1 5 1
202 2018 2 J 2002 323 435-545-552 443 10Cai 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 2015 12 Wiesbaden 12 911-915 4 CT 3 J 2013 2210 825-829 5 J 12Hwang Fengnan Cai Xiaochuan A parallel nonlinear additive Schwarz preconditioned inexact Newton algorithm for 2008 12 35 6923-6926 incompressible Navier-Stokes equations J Journal of 6Younis H FKaazempur-Mofrad M R Chung C et al Computational Physics 2005 2042 666-691 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 2003 318 995-1006 7Peng Hongmei Yang Dequan The boundary element analysis on Y bifurcation arterial hemodynamic characteristics J Chinese Journal of Medical Physics 2012 28 5 2937-2940 8Abdoulaev G Cadeddu S Delussu G et al ViVathe virtual vascular project J IEEE Transactions on Information Technology in Biomedicine 1998 24 268-274 J 9Qiao AikeGuo XinglingWu Shigui et al Numerical 2015 3 297-310 study of nonlinear pulsatile flow in S-shaped curved arteries J Medical Engineering and Physics 2004 267 Springer 1994 4717-30 11 Newton-Krylov-Schwarz J 2010 3712 90-92 preconditioner for general sparse linear systems J SI- AM Journal on Scientific Computing 1999 21 2 792-797 14 J 2016 46 7 915-928 15Panerai R B Dineen N E Brodie F G et al Spontaneous in cerebral blood flow regulationcontribution of PaCO 2 J Applied Physiology 2010 1096 1860-1868 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 330022 China 518055 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 2 12 10 6 mesh elements and the parallel efficiency is still around 72 43% Key wordshemodynamicsfinite element methodcomputational fluid dynamicsparallel computingdomain decomposition method