Flows of an incompressible Navier–Stokes fluid are frequently assumed to take place in domains whose boundaries are rigid and that the fluid adheres to them, i.e. there is the “no-slip” on the interface between the rigid solid and the flowing fluid. However, in many interesting problems the walls respond as (visco)-elastic structures and different slipping conditions on the fluid–structure interface seem to be more appropriate. Our main objective is to develop a reliable numerical approach capable of efficiently solving such fluid–structure interaction problems with Navier’s slip interface conditions in three dimensions. We focus on axi-symmetric flow problems; their two-dimensional character allows us to perform systematic testing of the performance of the solver and to study the effects of the (visco)-elasticity of the wall and the value of Navier’s slip-parameter on the properties of the flow including the vorticity, dissipation, pressure drop and wall shear stress. All tests concern steady and time-periodic flows in pipe-like domains with sinuses. It is startling that, in this geometric setting, the effects of (visco)-elasticity of the structure on the flow are minor in comparison to the setting when the walls are rigid.

中文翻译：

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粘弹性固体与纳维-斯托克斯流体之间具有纳维滑移界面条件的轴对称流动的流固数值求解器：可变形固体对流动特性的影响


不可压缩纳维-斯托克斯流体的流动通常被认为发生在边界是刚性的并且流体粘附在其上的域中，即刚性固体和流动流体之间的界面上存在“无滑移”。然而，在许多有趣的问题中，壁响应为（粘）弹性结构，并且流体-结构界面上的不同滑动条件似乎更合适。我们的主要目标是开发一种可靠的数值方法，能够有效解决三维纳维滑移界面条件下的流固耦合问题。我们专注于轴对称流动问题；它们的二维特性使我们能够对求解器的性能进行系统测试，并研究壁的（粘）弹性和纳维尔滑移参数值对流动属性（包括涡度）的影响，耗散、压降和壁面剪应力。所有测试都涉及带有窦的管状区域中的稳定且时间周期的流动。令人惊讶的是，在这种几何设置中，与壁刚性时的设置相比，结构的（粘）弹性对流动的影响较小。