Augmented Lagrangian method for constraining the shape of velocity profiles at outlet boundaries for three-dimensional finite element simulations of blood flow
Augmented Lagrangian method for constraining the shape of velocity profiles at outlet boundaries for three-dimensional finite element simulations of blood flow
复制标题
DOI：
10.1016/j.cma.2009.02.012
复制
发表时间：
2009-01-01
影响因子：
7.2
通讯作者：
Taylor, C. A.
中科院分区：
文献类型：
--
作者：
Kim, H. J.;Figueroa, C. A.;Taylor, C. A.
在心血管系统的三维血流模拟中，出口边界条件对计算域中的速度场和压力场有很大影响。这一事实促使新方法的发展，耦合三维计算域与一维数值模型，或者，与零维或一维的分析模型。在迄今为止所描述的所有这些方法中，无论它们是显式的还是隐式的，出口边界处的流量和压力之间的关系都是弱强制的。这种耦合不包括对速度剖面形状的任何约束，也不包括对界面处压力分布的任何约束。因此，仍然存在一些类别的问题，在最好的情况下，难以解决，在最坏的情况下，棘手的，与目前的数值方法模拟血液流动。这些问题包括在心动周期的一部分期间具有显著的流动逆转的问题或在计算域的出口附近的几何复杂性。我们已经实施了一种新的方法来解决这些具有挑战性的问题，其中一个增广拉格朗日方法是用来强制约束的上游计算域和下游分析域之间的接口处的速度剖面的形状。将这些对速度剖面形状的约束添加到耦合多域方法中，以隐式地将计算域与下游分析模型耦合。在这项研究中，一个轴对称的轮廓后，确保每个约束出口边界是圆形的。我们在这里证明，包括速度剖面的形状上的约束不影响速度和压力场，除了在受约束的出口边界附近。此外，这种新的方法，使问题的解决方案与无约束的方法分歧。(C)2009年由Elsevier B.V.出版
In three-dimensional blood flow simulations of the cardiovascular system, velocity and pressure fields in the computational domain are highly affected by outlet boundary conditions. This fact has motivated the development of novel methods to couple three-dimensional computational domains with one-dimensional numerical models or, alternatively, with zero-dimensional or one-dimensional analytic models. In all such methods described to date, whether they are explicit or implicit, the relationship between flow and pressure at the outlet boundary is enforced weakly. This coupling does not include any constraints on the shape of the velocity profiles nor on the distribution of pressure at the interface. As a result, there remain some classes of problems that are, at best, difficult to solve, and at worst, intractable, with current numerical methods for simulating blood flow. These include problems with significant flow reversal during part of the cardiac cycle or geometric complexity in the proximity of the outlet of the computational domain. We have implemented a novel method to resolve these challenging problems whereby an augmented Lagrangian method is used to enforce constraints on the shape of the velocity profile at the interface between the upstream computational domain and the downstream analytic domain. These constraints on the shape of the velocity profile are added to the Coupled Multidomain Method in order to implicitly couple the computational domain with downstream analytic models. In this study, an axi-symmetric profile is imposed after ensuring that each constrained outlet boundary is circular. We demonstrate herein that including constraints on the shape of the velocity profile does not affect velocity and pressure fields except in the immediate vicinity of the constrained outlet boundaries. Furthermore, this new method enables the solution of problems which diverged with an unconstrained method. (C) 2009 Published by Elsevier B.V.