基于Schwarz-Christoffel变换的非圆截面血管流场分布研究

应用Schwarz-Christoffel(S-C)变换方法，实现从复平面单位圆到多边形区域的共形映射，结合圆形管道下完全发展脉动流的Womersley算法理论，建立了基于S-C映射的非圆入口截面下的Womersley速度边界模型.在边界模型建立的基础上，应用计算流体力学方法，对基于生理真实的人体肺动脉二级分支血管在一个心动周期内的血流流动情况进行了数值模拟，并与通过外接圆管法设定入口速度边界条件得到的流场模拟结果进行了对比分析.分析结果表明，两者的模拟结果高度一致，但考虑到模拟效率和数值模拟结果的确定性，基于S-C映射的Womersley速度边界模型优于外接圆管方法，对于血管血流动力学的模拟研究更具有现实意义.

Research on the Flow Field Distribution of Non-Circular Cross-Section Vessels Based on the Schwarz-Christoffel Transformation

(With the Schwarz-Christoffel transformation method, a conformal mapping from a unit circle to a polygonal domain in the complex plane was obtained. Based on the mapping combined with the Womersley algorithm theory for fully developed pulsating flow in a circular pipe, a Womersley velocity boundary model with a non-circular inlet section was established. For this boundary model, the computational fluid dynamics (CFD) method was used to simulate the blood flow in the human pulmonary artery secondary branch based on physiological reality in a cardiac cycle, and the results were compared with those obtained from the connected circular tube method. The analysis of examples indicates that, the simulation results of the 2 methods are highly consistent, but in the aspects of simulation efficiency and certainty, the Womersley velocity boundary model based on the S-C mapping is better than the connected circular tube method, and has more practical significance for the simulation of vascular hemodynamics.