A modular numerical method for implicit 0D/3D coupling in cardiovascular finite element simulations
A modular numerical method for implicit 0D/3D coupling in cardiovascular finite element simulations
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DOI：
10.1016/j.jcp.2012.07.035
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发表时间：
2013-07-01
影响因子：
4.1
通讯作者：
Marsden, Alison L.
中科院分区：
文献类型：
--
作者：
Moghadam, Mahdi Esmaily;Vignon-Clementel, Irene E.;Marsden, Alison L.
由于循环系统复杂的动力学行为，心血管模拟中边界条件的实现带来了数值挑战。使用复杂的心脏和循环系统的闭环集总参数网络(LPN)模型作为计算流体动力学(CFD)模拟的边界条件，可以提供有价值的全局动态信息，特别是对于患者特定的模拟。本文给出了将任意LPN耦合到有限元Navier-Stokes求解器的必要公式。数值求解了电路模拟的闭环LPN，在界面处的0D和3D区域之间迭代传递压力和流动信息，从而产生时间隐式格式。对于Neumann边界，提出了一种隐式方法，而不考虑LPN，以获得期望的稳定性和收敛性质。描述了在零维域和三维域之间传递流动和压力信息的数值过程，并比较了隐式、半隐式和显式拟牛顿公式。通过一个稳定的边界公式解决了存在回流时的发散问题。文中还讨论了耦合Dirichlet边界条件的要求，并与Neumann耦合边界条件作了详细比较。具有在Dirichlet和Neumann耦合边界条件之间进行选择的选项，通过允许在3D-0D接口使用广泛的组件来增加当前框架的灵活性。(C)2012 Elsevier Inc.保留所有权利。
Implementation of boundary conditions in cardiovascular simulations poses numerical challenges due to the complex dynamic behavior of the circulatory system. The use of elaborate closed-loop lumped parameter network (LPN) models of the heart and the circulatory system as boundary conditions for computational fluid dynamics (CFD) simulations can provide valuable global dynamic information, particularly for patient specific simulations. In this paper, the necessary formulation for coupling an arbitrary LPN to a finite element Navier-Stokes solver is presented. A circuit analogy closed-loop LPN is solved numerically, and pressure and flow information is iteratively passed between the 0D and 3D domains at interface boundaries, resulting in a time-implicit scheme. For Neumann boundaries, an implicit method, regardless of the LPN, is presented to achieve the desired stability and convergence properties. Numerical procedures for passing flow and pressure information between the 0D and 3D domains are described, and implicit, semi-implicit, and explicit quasi-Newton formulations are compared. The issue of divergence in the presence of back-flow is addressed via a stabilized boundary formulation. The requirements for coupling Dirichlet boundary conditions are also discussed and this approach is compared in detail to that of the Neumann coupled boundaries. Having the option to select between Dirichlet and Neumann coupled boundary conditions increases the flexibility of current framework by allowing a wide range of components to be used at the 3D-0D interface. (c) 2012 Elsevier Inc. All rights reserved.