Full and Hybrid Multiscale Lubrication Modeling

Abstract

The numerical solution for the lubrication of parallel rough surfaces cannot be obtained using the well-known flow factors of Patir and Cheng. Nor can it be determined using homogenization techniques. Is there an alternative, besides a purely long-term deterministic way of solving the problem? The present paper aims at proposing a multiscale approach in order to reduce the computing time, specific to deterministic resolutions, while maintaining good accuracy. The configuration is a parallel rough surface slider, with imposed hydrodynamic operating conditions. The domain consists of independent macro-elements, on which the Reynolds equation is solved. Then, the macro-element boundaries are adjusted to ensure global mass conservation. In its hybrid version, the algorithm replaces some well-chosen macro-elements by simple linear finite elements. The results clearly show the potential of our method. Because the lubrication of each macro-element can be processed independently, the multicore architecture of the processor is exploited. Even if the performance depends on the ratio roughness/height, the computing time is half than for the classical deterministic method, with a few percent errors. The work concludes with some recommendations on the configurations for which the multiscale method is best suited, such as surfaces with short correlation lengths.