Kim T, Cheer A Y, Dwyer H A
Department of Mathematics, University of California, One Shields Avenue, Davis, CA 95616, USA.
J Biomech. 2004 Aug;37(8):1125-36. doi: 10.1016/j.jbiomech.2003.12.028.
A numerical dye method for the visualization of unsteady three-dimensional flow calculations is introduced by coupling the unsteady convection-diffusion equation to the Navier-Stokes equation for mass and momentum. This system of equations is descretized using a finite volume projection-like algorithm with generalized coordinates and overset grids. A powerful pressure prediction method is used to accelerate the convergence of the Pressure Poisson equation. To demonstrate the visualization technique, blood flow through the aortic arch region and the three main arterial branches is computed using various Womersley numbers. In this technique, parcels of fluid are followed in time as a function of the cardiac cycle without having to track individual particles, which in turn aids us to better understand some important aspects of the three-dimensionality of the developing unsteady flow. Using this numerical dye method we analyze the strength of the cross flow during the cardiac cycle, the relationship between the penetration of blood into the aortic branches from its relative position in the ascending aortic region and the effects of the Womersley parameter. This technique can be very useful in the design and development of stents where the topology of the device would require understanding where the blood emanating from the heart ends up at the end of the cardiac cycle. Moreover, this method could be useful in investigating the influence of flow and geometry on the local introduction of medication.
通过将非定常对流扩散方程与质量和动量的纳维-斯托克斯方程相耦合，引入了一种用于非定常三维流动计算可视化的数值染色方法。该方程组采用具有广义坐标和重叠网格的有限体积投影类算法进行离散化。使用一种强大的压力预测方法来加速压力泊松方程的收敛。为了演示可视化技术，使用各种沃默斯利数计算了通过主动脉弓区域和三条主要动脉分支的血流。在该技术中，流体微团随时间跟踪，作为心动周期的函数，而无需跟踪单个粒子，这反过来有助于我们更好地理解发展中的非定常流动三维性的一些重要方面。使用这种数值染色方法，我们分析了心动周期中横流的强度、血液从升主动脉区域的相对位置进入主动脉分支的渗透情况与沃默斯利参数的影响之间的关系。这种技术在支架的设计和开发中可能非常有用，因为装置的拓扑结构需要了解心脏流出的血液在心动周期结束时最终流向何处。此外，该方法在研究流动和几何形状对局部药物引入的影响方面可能也很有用。
