基于大涡模拟的血流动力学并行区域分解算法

The most common cause of cardiovascular and cerebrovascular diseases is change of hemodynamic. At present, relevant research has gradually focused on the influence of turbulent shear stress, structure, separation and other turbulence characteristics on the disease, not only the average velocity and pressure field. Due to the complex and multi-scale geometry of the vessels, as well as the pulsation effect of the heart, when solving the high-precision turbulence model simulation such as large eddy simulation, the large scale and nonlinear feature are the major challenge of the algorithm. As a result, the high scalable parallel algorithms for large eddy simulation of blood flows are quite demanding. In this project,we plan to develop a new highly scalable implicit solver for the large eddy simulation of 3D turbulent blood flow on unstructured meshes.We shall use a stabilized Galerkin finite element method for the spatial approximation of the problem, and a implicit method for the time discretization. We would design a parallel scalable domain decomposition method by using the Newton-Krylov-Schwarz algorithm and the multigrid method to solve the nonlinear algebraic system arising from the discretization, with emphasis on the robustness and the parallel scalability. The proposed solver is expected to be scalable up to more than 10,000 processor cores on the platform of multi-core architecture, and thus can meet the computing needs of relevant researches and clinical requirements.

血流动力学性能的改变是诱发心脑血管疾病的主要原因。目前相关研究逐渐从关注稳态速度场、压力场分布深入至湍流结构、流动分离再附与回流以及涡旋剪切力等湍动参数对疾病的影响。人体血管网络高度复杂且呈几何多尺度，加之心脏的脉动效应，采用大涡模拟等高精度湍流模型仿真时，计算规模与复杂度对求解算法提出挑战，因此具有高扩展并行性能的算法在血流动力学研究中有着重大需求。目前相关并行算法的研究尚远远跟不上超级计算机硬件发展水平，血流模拟商业软件只能达到百核量级的并行规模。基于上述背景，本项目研究血流大涡模拟的全隐格式与非结构有限元离散方法、多水平型Newton-Krylov-Schwarz算法及预处理技术，重点关注算法的鲁棒性与并行可扩展性能。同时兼顾大规模并行计算平台架构程序优化技术，目的是开发可扩展至数万处理器核的并行求解算法，以期实现血流复杂湍动流场的高精度、高时效性仿真，满足相关研究及临床需求。

血流动力学功能的改变可诱发多类疾病。目前以计算流体力学技术为基础的血流动力学数值模拟技术逐步发展至瞬态、湍动模拟。由于血管网复杂且呈多尺度，受心脏脉动效应的影响，人体的血流动力学大涡模拟带来了巨量计算难题。为充分利用目前超算平台资源，快速高效地求解血流动力学模拟问题，本项目研究血流大涡模拟的全隐格式与非结构有限元离散方法、多水平型Newton-Krylov-Schwarz算法及预处理技术以及大规模并行计算平台架构程序优化技术，开发可扩展至数万处理器核的血流模拟并行算法，以实现血流复杂湍动流场的高精度、高时效性仿真。

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