Wave propagation models in the time domain have been extensively used in the available literature to study the flow characteristics in blood vessels. Most of the wave propagation models have considered flat or parabolic velocity profile functions to estimate the nonlinear convection and diffusion terms present in the conservation of momentum equation. There are only a few works available on the wave propagation analysis in which the velocity profile is approximated using different polynomial functions. In this study, a computationally efficient nonlinear axisymmetric formulation is presented without a priori assumed velocity profile function across the cross section to model the blood flow. Such a formulation in terms of axial velocity (u), pressure (p), and domain radius (R) facilitates the evolution/development of axial velocity profile as the flow progresses with time. The arterial mechanical behavior is modeled using a linear elastic constitutive relation. Partial differential equations are discretized using the finite element method and the Galerkin time integration technique in space and time domains, respectively. This study finds a phase difference between the shear stress at the wall and the flow rate. The flow characteristics and the velocity profile function are found to be in good agreement with the three-dimensional computational results available in the literature. The detailed investigation of the axial velocity across the cross section reveals neither flat nor parabolic profiles, as previously assumed in the literature.

中文翻译：

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变形血管中波传播的轴向速度分布的基准研究

时域中的波传播模型已广泛用于现有文献中，以研究血管中的流动特性。大多数波传播模型已经考虑了平面或抛物线速度分布函数，以估计动量方程守恒中存在的非线性对流和扩散项。在波传播分析中只有少数著作可用不同的多项式函数来近似速度分布。在这项研究中，提出了一种计算效率高的非线性轴对称公式，该公式没有事先假设的横截面速度分布函数来对血流进行建模。以轴向速度（u），压力（p），并且随着流动的进行，畴半径（R）促进了轴向速度分布图的发展/发展。使用线性弹性本构关系对动脉力学行为进行建模。分别使用时域和时域有限元方法和Galerkin时间积分技术离散偏微分方程。这项研究发现了墙体处的剪切应力与流速之间的相位差。发现流动特性和速度分布函数与文献中可获得的三维计算结果非常吻合。如先前在文献中所假设的那样，对横截面的轴向速度的详细研究既没有显示出平坦的轮廓也没有显示出抛物线轮廓。