一种新的任意截面二维血流模型
A new two-dimensional blood flow model with arbitrary cross sections
摘要：
本文导出了一种新的任意截面动脉中血液流动的二维模型。该模型包括一个系统的平衡定律的质量守恒和平衡的动量在轴向和角向方向。该方程是通过对大、窄容器中的不可压缩Navier-斯托克斯方程进行渐近分析并在每个截面中沿径向积分而得到的。讨论了该方程组的主要性质，并给出了一个保正平衡的中心迎风格式。该计划的优点将在各种情况下进行测试。特别是，使用理想化的主动脉模型的模拟的数值结果示出。我们分析了在不同的初始条件下，如扰动的血管壁中的隆起组成的稳定状态下的血流的时间演化。我们考虑不同的情况下，由不同的变化，在船舶的弹性。
英文摘要：
A new two-dimensional model for blood flows in arteries with arbitrary cross sections is derived. The model consists of a system of balance laws for conservation of mass and balance of momentum in the axial and angular directions. The equations are derived by applying asymptotic analysis to the incompressible Navier-Stokes equations in narrow, large vessels and integrating in the radial direction in each cross section. The main properties of the system are discussed and a positivity-preserving well-balanced central-upwind scheme is presented. The merits of the scheme will be tested in a variety of scenarios. In particular, numerical results of simulations using an idealized aorta model are shown. We analyze the time evolution of the blood flow under different initial conditions such as perturbations to steady states consisting of a bulging in the vessel's wall. We consider different situations given by distinct variations in the vessel's elasticity.
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