A Reduced Basis Method for the Homogenized Reynolds Equation Applied to Textured Surfaces (Communications in Computational Physics, 2018)
In fluid film lubrication investigations, the homogenized Reynolds equation is used as an averaging model to deal with microstructures induced by roughor textured surfaces. The objective is a reduction of computation time compared todirectly solving the original Reynolds equation which would require very fine computational grids. By solving cell problems on the microscale, homogenized coefficientsare computed to set up a homogenized problem on the macroscale. For the latter,the discretization can be chosen much coarser than for the original Reynolds equation. However, the microscale cell problems depend on the macroscale film thicknessand thus become parameter-dependent. This requires a large number of cell problemsto be solved, contradicting the objective of accelerating simulations. A reduced basismethod is proposed which significantly speeds up the solution of the cell problems andthe computation of the homogenized coefficients without loss of accuracy. The suitability of both the homogenization technique and the combined homogenization/reducedbasis method is documented for the application to textured journal bearings. For thispurpose, numerical results are presented where deviations from direct solutions of theoriginal Reynolds equation are investigated and the reduction of computational cost ismeasured.
Keywords: Multiscale problems; homogenization; reduced basis method; Reynolds equation; lubrication; tribology.