Chen Rongliang, Wu Bokai, Cheng Zaiheng, Shiu Wen-Shin, Liu Jia, Liu Liping, Wang Yongjun, Wang Xinhong, Cai Xiao-Chuan
Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China.
Shenzhen Key Laboratory for Exascale Engineering and Scientific Computing, Shenzhen, China.
Int J Numer Method Biomed Eng. 2020 Nov;36(11):e3392. doi: 10.1002/cnm.3392. Epub 2020 Aug 28.
Numerical simulation of blood flows in patient-specific arteries can be useful for the understanding of vascular diseases, as well as for surgery planning. In this paper, we simulate blood flows in the full cerebral artery of stroke patients. To accurately resolve the flow in this rather complex geometry with stenosis is challenging and it is also important to obtain the results in a short amount of computing time so that the simulation can be used in pre- and/or post-surgery planning. For this purpose, we introduce a highly scalable, parallel non-nested two-level domain decomposition method for the three-dimensional unsteady incompressible Navier-Stokes equations with an impedance outlet boundary condition. The problem is discretized with a stabilized finite element method on unstructured meshes in space and a fully implicit method in time, and the large nonlinear systems are solved by a preconditioned parallel Newton-Krylov method with a two-level Schwarz method. The key component of the method is a non-nested coarse problem solved using a subset of processor cores and its solution is interpolated to the fine space using radial basis functions. To validate and verify the proposed algorithm and its highly parallel implementation, we consider a case with available clinical data and show that the computed result matches with the measured data. Further numerical experiments indicate that the proposed method works well for realistic geometry and parameters of a full size cerebral artery of an adult stroke patient on a supercomputers with thousands of processor cores.
针对特定患者动脉内血液流动的数值模拟，对于理解血管疾病以及手术规划都可能是有用的。在本文中，我们模拟了中风患者全脑动脉内的血液流动。要在这种具有狭窄的相当复杂的几何形状中精确求解流动是具有挑战性的，并且在短计算时间内获得结果也很重要，以便该模拟可用于手术前和/或手术后的规划。为此，我们针对具有阻抗出口边界条件的三维非定常不可压缩纳维 - 斯托克斯方程，引入了一种高度可扩展的并行非嵌套两级区域分解方法。该问题在空间上用非结构化网格上的稳定有限元方法离散，在时间上用全隐式方法离散，并且通过具有两级施瓦茨方法的预处理并行牛顿 - 克里洛夫方法求解大型非线性系统。该方法的关键组件是使用一部分处理器核心求解的非嵌套粗问题，其解使用径向基函数插值到细网格空间。为了验证和检验所提出的算法及其高度并行实现，我们考虑一个具有可用临床数据的案例，并表明计算结果与测量数据相匹配。进一步的数值实验表明，所提出的方法在具有数千个处理器核心的超级计算机上，对于成年中风患者全尺寸脑动脉的实际几何形状和参数能很好地工作。
