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.

中文翻译：

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变换变量对流反应系统的时空最小二乘有限元法

我们提出了一种基于最小二乘有限元法 (LSFEM) 来求解对流反应系统的方法。对于稳态计算，通过一个简单的例子说明和演示了与再循环流相关的问题。即使生成项很小，该方法也可以计算开放流中的浓度分布。这是估计血液中溶血的情况。与时间相关的流动是用时空 LSFEM 离散化计算的。我们观察到计算的血红蛋白浓度在流动的某些区域可能变为负值；这是生理上无法接受的结果。为了防止这种情况，我们提出了变量的二次变换。转换后的控制方程可以通过 LSFEM 以直接的方式求解，没有非物理行为的迹象。