论文标题
一个新的薄层模型，用于附近两个非静态表面之间的粘性流量
A new thin layer model for viscous flow between two nearby non-static 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。我们使用溶液的形式渐近扩展显示，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。对新模型和Navier-Stokes方程的正式渐近扩展的主要项是相同极限问题的解决方案，并且极限问题的类型取决于边界条件。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的表面上都知道拖网和摩擦力，则极限是薄流体层模型的解决方案。该模型已获得是计算附近两个移动表面之间粘性流体流量的有价值的工具，而无需先验确定该流量是否是润滑或薄流体层问题的典型的流动，并且如果没有巨大的计算努力，而无需将这种较薄域中的Navier-Stokes方程式所需的巨大计算努力。
We propose a two-dimensional flow model of a viscous fluid between two close moving surfaces. We show, using a formal asymptotic expansion of the solution, 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 leading term of the formal asymptotic expansions of the solutions to the new model and Navier-Stokes equations are solution of the same limit problem, and the type of the limit problem depends on the boundary conditions. If slip velocity boundary conditions are imposed on the upper and lower bound surfaces, the limit is a solution of a lubrication model, but if the tractions and friction forces are known on both bound surfaces, the limit is a solution of a thin fluid layer model. The model proposed has been obtained to be a valuable tool for computing viscous fluid flow between two nearby moving surfaces, without the need to decide a priori whether the flow is typical of a lubrication or a thin fluid layer problem, and without the enormous computational effort that would be required to solve the Navier-Stokes equations in such a thin domain.
