Laboratório Nacional de Computação Científica, Av. Getúlio Vargas 333, Quitandinha, 25651-075 Petrópolis, Brazil.
Int J Numer Method Biomed Eng. 2013 Mar;29(3):408-27. doi: 10.1002/cnm.2519. Epub 2012 Nov 6.
This work presents a generic and efficient black-box approach for the strong iterative coupling of dimensionally heterogeneous flow models in computational hemodynamics. A heterogeneous model of the cardiovascular system is formed by several vascular black-box components, which are connected through coupling equations. The associated system of equations is solved using the Broyden algorithm. In addition, a multiple time-stepping strategy is introduced to meet different component requirements. The proposed algorithm is employed to split a 3D-1D-0D closed-loop model of the cardiovascular system into corresponding black-box components standing for the 3D (specific vessels), 1D (systemic arteries/peripheral vessels), and 0D (venous/cardiac/pulmonary circulation) components. Examples of application are presented showing the robustness and suitability of this novel approach.
本工作提出了一种通用且高效的黑盒方法，用于计算血液动力学中具有不同维度的流动模型的强迭代耦合。心血管系统的异构模型由几个血管黑盒组件组成，这些组件通过耦合方程连接。使用 Broyden 算法求解相关方程组。此外，还引入了一种多重时间步长策略来满足不同组件的要求。所提出的算法用于将心血管系统的 3D-1D-0D 闭环模型分解为相应的黑盒组件，代表 3D（特定血管）、1D（系统动脉/外周血管）和 0D（静脉/心脏/肺循环）组件。给出了应用实例，展示了这种新方法的健壮性和适用性。
