An effective Navier-Stokes model for the simulation of textured surface lubrication

For a wide range of applications in the context of textured surface lubrication, both the Reynolds equation and the Stokes system are not valid. When it comes to flows with high velocities and surfaces with deep textures of moderate length, the Navier-Stokes equations have to be solved instead. For this kind of applications, a new effective model is presented which is derived from an upscaling technique applied to the incompressible Navier-Stokes equations. It provides more accurate results than the Reynolds or Stokes problem. In addition, the computational cost compared with solving the Navier-Stokes system is reduced significantly. Numerical results for two- and three-dimensional test cases demonstrate the accuracy and efficiency of the approach.