论文标题
通过柔性墙的通道模型的数学分析
Mathematical Analysis of a Model of Blood Flow through a Channel with Flexible Walls
论文作者
论文摘要
本研究致力于在带有柔性壁的通道中移动流体流动的稳定性问题，并与壁相互作用，墙壁可能会受到行进波。实验数据表明，流动流体的能量可以被结构（墙壁）传递和消耗，从而引起“行进波弹力”。流体结构相互作用的稳定性分为两个部分：（i）通道中流体流动的稳定性，并谐波移动的壁和（ii）固体结构的稳定性与流量一起参与能量交换。流体流的稳定性是研究的主要重点。结果表明，使用质量保护和不可压缩条件，可以获得流函数的初始边界值问题。边界条件反映了以下事实：（i）对于轴对称流，沿对称的轴垂直方向没有运动，并且（ii）（ii）近边界流与结构之间没有相对运动（“无滑动”条件）。封闭形式的解决方案以无限功能系列的形式得出并表示。
The present research is devoted to the problem of stability of the fluid flow moving in a channel with flexible walls and interacting with the walls, which are subject to traveling waves. Experimental data shows that the energy of the flowing fluid can be transferred and consumed by the structure (the walls), which induces "traveling wave flutter." The problem of stability of fluid-structure interaction splits into two parts: (i) stability of fluid flow in the channel with harmonically moving walls and (ii) stability of solid structure participating in the energy exchange with the flow. Stability of fluid flow is the main focus of the research. It is shown that using the mass conservation and the incompressibility condition one can obtain the initial boundary value problem for the stream function. The boundary conditions reflect the facts that (i) for the axisymmetrical flow, there is no movement in the vertical direction along the axis of symmetry, and (ii) there is no relative movement between the near boundary flow and the structure ("no-slip" condition). The closed form solution is derived and represented in the form of an infinite functional series.
