Homogenization of Reynolds Equation by Two-Scale Convergence

在不同机器元素增加水动力学表演，作为例如。杂志轴承和戳轴承，在润滑油期间，理解表面粗糙的影响是重要的。在这个连接，一个人遇到茶碱的 homogenization 可压缩的雷纳兹方程，在润滑表面的粗糙被假定周期的地方。这个问题最近被使用多重规模扩大的形式化方法在更面向工程的报纸学习了。在这篇论文，我们严厉地由使用二规模的集中证明两 homogenizationand 是修正者结果，它可以被认为是上面描述的正式多重规模扩大方法的一个理由。而且，一些数字插图和结果被介绍。

To increase the hydrodynamic performance in different machine elements, as e.g. journal bearings and thrust bearings, during lubrication it is important to understand the influence of surface roughness. In this connection one encounters homogenization of the incompressible Reynolds equation, where the roughness of the lubricated surface is assumed to be periodic. This problem has recently been studied in more engineering- oriented papers by using the formal method of multiple scale expansion. In this paper, we rigorously prove both homogenization and corrector results by using two-scale convergence, which may be regarded as a justification of the formal multiple scale expansion method described above. Moreover, some numerical illustrations and results are presented.