Nam Jaewook, Behr Marek, Pasquali Matteo
Department of Chemical & Biomolecular Engineering and Ken Kennedy Institute for Information Technology Rice University, Houston, Texas 77005, USA.
Comput Methods Appl Mech Eng. 2011 Aug 1;200(33-36):2562-2576. doi: 10.1016/j.cma.2011.04.015.
We present a method to solve a convection-reaction system based on a least-squares finite element method (LSFEM). For steady-state computations, issues related to recirculation flow are stated and demonstrated with a simple example. The method can compute concentration profiles in open flow even when the generation term is small. This is the case for estimating hemolysis in blood. Time-dependent flows are computed with the space-time LSFEM discretization. We observe that the computed hemoglobin concentration can become negative in certain regions of the flow; it is a physically unacceptable result. To prevent this, we propose a quadratic transformation of variables. The transformed governing equation can be solved in a straightforward way by LSFEM with no sign of unphysical behavior. The effect of localized high shear on blood damage is shown in a circular Couette-flow-with-blade configuration, and a physiological condition is tested in an arterial graft flow.
我们提出了一种基于最小二乘有限元法（LSFEM）求解对流反应系统的方法。对于稳态计算，阐述了与再循环流相关的问题，并通过一个简单示例进行了说明。即使生成项很小时，该方法也能计算开放流中的浓度分布。在估计血液中的溶血情况时就是这种情况。随时间变化的流采用时空LSFEM离散化进行计算。我们观察到，计算得到的血红蛋白浓度在流的某些区域可能变为负值；这是一个物理上不可接受的结果。为防止这种情况，我们提出了变量的二次变换。变换后的控制方程可以通过LSFEM以直接的方式求解，且没有非物理行为的迹象。在带有叶片的圆形库埃特流配置中展示了局部高剪切对血液损伤的影响，并在动脉移植流中测试了一种生理状况。
