论文标题
两个移动表面之间的薄粘性流体膜的新流量模型
A new flow model for a thin viscous fluid film between two moving surfaces
论文作者
论文摘要
我们提出了两个紧密移动表面之间粘性流体的二维流量模型。我们表明，当两个表面之间的距离趋于零时，其渐近行为与Navier-Stokes方程的距离相同。新模型和Navier-Stokes方程的解决方案会收敛到相同的极限问题，这取决于边界条件。如果将滑动速度边界条件施加在上层和下限表面上，则极限是润滑模型的解决方案，但是如果在两个结合表面上都知道了街道和摩擦力，则极限是浅水模型的解决方案。提出的模型已获得是计算两个近距离移动表面之间粘性流体流量的有价值的工具，而无需先验地确定该流量是否是润滑问题的典型特征，还是它是浅水水类型的，并且没有巨大的计算努力，即可在此类稀薄的domain中不需要近溶液的溶方法。
We propose a two-dimensional flow model of a viscous fluid between two close moving surfaces. We show that its asymptotic behavior, when the distance between the two surfaces tends to zero, is the same as that of the the Navier-Stokes equations. The solutions of the new model and Navier-Stokes equations converge to the same limit problem, that depends on the boundary conditions. If slip velocity boundary conditions are imposed on the upper and lower bound surfaces, the limit is solution of a lubrication model, but if the tractions and friction forces are known on both bound surfaces, the limit is solution of a shallow water model. The model proposed has been obtained to be a valuable tool for computing viscous fluid flow between two close moving surfaces, without the need to decide a priori whether the flow is typical of a lubrication problem or it is of shallow water type, and without the enormous computational effort that would be required to solve the Navier-Stokes equations in such a thin domain.
