In a companion study \cite{patterson2020computing2D}, we present a numerical method for simulating 2D viscous flow through an open compliant closed channel, drive by pressure gradient. We consider the highly viscous regime, where fluid dynamics is described by the Stokes equations, and the less viscous regime described by the Navier-Stokes equations. In this study, we extend the method to 3D tubular flow. The problem is formulated in axisymmetric cylindrical coordinates, an approach that is natural for tubular flow simulations and that substantially reduces computational cost. When the elastic tubular walls are stretched or compressed, they exert forces on the fluid. These singular forces introduce unsmoothness into the fluid solution. As in the companion 2D study \cite{patterson2020computing2D}, we extend the immersed interface method to an open tube, and we compute solution to the model equations using the resulting method. Numerical results indicate that this new method preserves sharp jumps in the solution and its derivatives, and converges with second-order accuracy in both space and time.
翻译:在一项配套研究 \ cite{ patterson2020computing2D}中,我们提出了一个模拟 2D 粘结通过一个开放的封闭通道流的数值方法,由压力梯度驱动。我们考虑了高粘度系统,其中流体动态由斯托克斯方程式描述,以及纳维耶-斯托克斯方程式描述的较低粘度系统。在这个研究中,我们将该方法扩大到3D 管流。问题是在轴对立的圆柱体坐标上形成的,这是一种对管流模拟的自然方法,可以大幅降低计算成本。当弹性管壁被拉长或压缩时,它们会将力压在液体上。这些奇特的力量将不透性引入液体溶液溶液中。正如在伴头的2D 研究 \ cite{ patterson20compupping2D} 中一样,我们将浸透的界面方法扩大到一个开口管,我们用由此得出的方法对模型方形的解析解决方案。第二个数字结果显示,这一新方法既保持了时间的精确度,也保持了空间的精确度。