Abraham Feby, Behr Marek, Heinkenschloss Matthias
University of Pennsylvania, Mechanical Engineering and Applied Mechanics, Philadelphia, PA 19104, USA.
Comput Methods Biomech Biomed Engin. 2005 Jun;8(3):201-12. doi: 10.1080/10255840500309562.
This paper presents a numerical study of non-Newtonian effects on the solution of shape optimization problems involving unsteady pulsatile blood flow. We consider an idealized two dimensional arterial graft geometry. Our computations are based on the Navier-Stokes equations generalized to non-Newtonian fluid, with the modified Cross model employed to account for the shear-thinning behavior of blood. Using a gradient-based optimization algorithm, we compare the optimal shapes obtained using both the Newtonian and generalized Newtonian constitutive equations. Depending on the shear rate prevalent in the domain, substantial differences in the flow as well as in the computed optimal shape are observed when the Newtonian constitutive equation is replaced by the modified Cross model. By varying a geometric parameter in our test case, we investigate the influence of the shear rate on the solution.
本文对非牛顿效应影响涉及非稳态脉动血流的形状优化问题的解进行了数值研究。我们考虑一个理想化的二维动脉移植几何形状。我们的计算基于推广到非牛顿流体的纳维-斯托克斯方程，采用修正的Cross模型来考虑血液的剪切变稀行为。使用基于梯度的优化算法，我们比较了使用牛顿本构方程和广义牛顿本构方程获得的最优形状。根据域中普遍存在的剪切速率，当用修正的Cross模型代替牛顿本构方程时，在流动以及计算得到的最优形状方面会观察到显著差异。通过改变我们测试案例中的一个几何参数，我们研究了剪切速率对解的影响。
