论文标题
使用滑移边界条件解决D'Alembert的悖论：摩擦参数对阻力系数的影响
Resolution of d'Alembert's paradox using slip boundary conditions: The effect of the friction parameter on the drag coefficient
论文作者
论文摘要
d'Alembert的悖论是矛盾的观察结果，即对于不可压缩的（潜在的）流体流动，相对于流体，具有恒定速度的身体没有拖曳力。通过考虑Navier的滑动边界条件，可以直接解决此悖论。然后，围绕圆柱体的电势流解决Navier-使用摩擦参数$β=-2ν$稳定方程。这种负摩擦参数可以物理解释为流体被气缸壁加速。这解释了缺乏阻力。 在本文中，我们介绍了Navier滑动边界条件，并表明选择了摩擦参数阳性分辨率D'Alembert的悖论。然后，我们进一步研究了摩擦参数$β$对阻力系数的影响。特别是，我们表明，对于大$β$，阻力系数与实验值很好。此外，我们提供了数值证据，表明牛顿延续方法（从小雷诺的数字转移到大型）需要更少的迭代才能成功。因此，从计算角度来看，滑动边界条件也是有利的。
d'Alembert's paradox is the contradictory observation that for incompressible and inviscid (potential) fluid flow, there is no drag force experienced by a body moving with constant velocity relative to the fluid. This paradox can be straightforwardly resolved by considering Navier's slip boundary condition. Potential flow around a cylinder then solves the Navier--Stokes equations using friction parameter $β=-2ν$. This negative friction parameter can be interpreted physically as the fluid being accelerated by the cylinder wall. This explains the lack of drag. In this paper, we introduce the Navier slip boundary condition and show that choosing the friction parameter positive resolves d'Alembert's paradox. We then further examine the effect of the friction parameter $β$ on the drag coefficient. In particular, we show that for large $β$ the drag coefficient corresponds well with experimental values. Moreover, we provide numerical evidence that the Newton continuation method (moving from small to large Reynold's numbers) requires fewer iterations to succeed. Thus the slip boundary condition is advantageous also from a computational perspective.
