Kuprat A P, Kabilan S, Carson J P, Corley R A, Einstein D R
Fundamental and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, WA.
J Comput Phys. 2013 Jul;244. doi: 10.1016/j.jcp.2012.10.021.
In this study, we present a novel multiscale computational framework for efficiently linking multiple lower-dimensional models describing the distal lung mechanics to imaging-based 3D computational fluid dynamics (CFD) models of the upper pulmonary airways in order to incorporate physiologically appropriate outlet boundary conditions. The framework is an extension of the Modified Newton's Method with nonlinear Krylov accelerator developed by Carlson and Miller [1, 2, 3]. Our extensions include the retention of subspace information over multiple timesteps, and a special correction at the end of a timestep that allows for corrections to be accepted with verified low residual with as little as a single residual evaluation per timestep on average. In the case of a single residual evaluation per timestep, the method has zero additional computational cost compared to uncoupled or unidirectionally coupled simulations. We expect these enhancements to be generally applicable to other multiscale coupling applications where timestepping occurs. In addition we have developed a "pressure-drop" residual which allows for stable coupling of flows between a 3D incompressible CFD application and another (lower-dimensional) fluid system. We expect this residual to also be useful for coupling non-respiratory incompressible fluid applications, such as multiscale simulations involving blood flow. The lower-dimensional models that are considered in this study are sets of simple ordinary differential equations (ODEs) representing the compliant mechanics of symmetric human pulmonary airway trees. To validate the method, we compare the predictions of hybrid CFD-ODE models against an ODE-only model of pulmonary airflow in an idealized geometry. Subsequently, we couple multiple sets of ODEs describing the distal lung to an imaging-based human lung geometry. Boundary conditions in these models consist of atmospheric pressure at the mouth and intrapleural pressure applied to the multiple sets of ODEs. In both the simplified geometry and in the imaging-based geometry, the performance of the method was comparable to that of monolithic schemes, in most cases requiring only a single CFD evaluation per time step. Thus, this new accelerator allows us to begin combining pulmonary CFD models with lower-dimensional models of pulmonary mechanics with little computational overhead. Moreover, because the CFD and lower-dimensional models are totally separate, this framework affords great flexibility in terms of the type and breadth of the adopted lower-dimensional model, allowing the biomedical researcher to appropriately focus on model design.
在本研究中，我们提出了一种新颖的多尺度计算框架，用于有效地将多个描述远端肺力学的低维模型与基于成像的上呼吸道三维计算流体动力学（CFD）模型相连接，以便纳入生理上合适的出口边界条件。该框架是Carlson和Miller [1, 2, 3] 开发的带有非线性Krylov加速器的修正牛顿法的扩展。我们的扩展包括在多个时间步长上保留子空间信息，以及在时间步长结束时进行特殊校正，该校正允许以经验证的低残差接受校正，平均每个时间步长只需进行一次残差评估。在每个时间步长进行一次残差评估的情况下，与非耦合或单向耦合模拟相比，该方法的额外计算成本为零。我们期望这些增强功能通常适用于其他存在时间步长的多尺度耦合应用。此外，我们还开发了一种 “压降” 残差，它允许在三维不可压缩CFD应用和另一个（低维）流体系统之间实现稳定的流耦合。我们期望这种残差对于耦合非呼吸性不可压缩流体应用（例如涉及血流的多尺度模拟）也很有用。本研究中考虑的低维模型是一组简单的常微分方程（ODEs），代表对称的人类肺气道树的顺应性力学。为了验证该方法，我们将CFD - ODE混合模型的预测结果与理想化几何形状中仅含ODE的肺气流模型进行了比较。随后，我们将多组描述远端肺的ODE与基于成像的人类肺几何形状相耦合。这些模型中的边界条件包括口腔处的大气压力和应用于多组ODE的胸膜腔内压。在简化几何形状和基于成像的几何形状中，该方法的性能与整体方案相当，在大多数情况下每个时间步长仅需进行一次CFD评估。因此，这种新的加速器使我们能够以很少的计算开销开始将肺CFD模型与肺力学的低维模型相结合。此外，由于CFD模型和低维模型是完全分开的，该框架在采用的低维模型的类型和广度方面提供了极大的灵活性，使生物医学研究人员能够适当地专注于模型设计。
