**4. E**ff**ect of Multi-Scale Textures on Friction and Wear—Numerical Approaches**

The design of optimum surface textures devised to improve the tribological performance of contacting interfaces can be considerably improved by using numerical simulation tools. Using numerical approaches to simulate the frictional behavior of multi-scale textures, the interplay of several physical factors (i.e., thermal effects, complex rheology, asperity contacts, surface wettability and the intricate lubricant flow as well as percolation) acting simultaneously on different lengths scales in the tribological contact zone can be investigated to facilitate the design of effective multi-scale textures. Complementary, numerical results can be useful to shed light on the underlying mechanisms responsible for the observed friction and wear reduction (e.g., micro-hydrodynamic bearing, inlet-suction, oil reservoir, and debris trapping effects), the improved sealing performance (e.g., lubricant channeling and percolation effects) and the finer contact temperature control induced by multi-scale textures. Therefore, optimum texture parameters (e.g., texture shape, size, depth, density) could be determined for specific applications and working conditions.

In this regard, three main modeling approaches, namely (i) computational fluid dynamics (CFD), (ii) Reynolds-type equation formulations based upon deterministic and averaging/homogenization methods, and (iii) numerical multi-scale techniques, are frequently used to simulate the tribological behavior of textured surfaces in different lubrication regimes. It is important to notice that not all modeling approaches presented in the following sections have already been applied specifically to the simulation of multi-scale textures. Nevertheless, most of the discussed methods and techniques can be extended to accomplish advanced analysis concerning the lubrication performance of contact interfaces with multi-scale textures. Thus, this review also intends to pave the way for future developments of more sophisticated approaches to model multi-scale surface textures.
