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Superhydrophobic surfaces with a slip effect have been proven to be effective to achieve surface drag reduction. In this paper, we fabricated superhydrophobic disks via laser ablation and chemical modification, and their drag-reduction performance is tested by a rheometer. However, the superhydrophobic disk achieves a limited drag-reduction effect (33.5% in maximum) with poor consistency (decay rapidly as rotating speed increases). To enhance the drag-reduction performance of the superhydrophobic surfaces, surfaces with tunable patterns consisting of superhydrophobic and hydrophobic surfaces are proposed. The difference in wettability and slip length between different regions is employed to control the flow direction. The effect of different patterns is investigated both experimentally and numerically, and the results indicate that the pattern distribution performs a great impact on the drag-reduction effect. The pattern consistent with the primary flow can not only enhance the effect (60.3% in maximum) but also the consistency (maintained at a higher rotating speed) of drag-reduction. On the contrary, the pattern perpendicular to the flow direction is harmful to drag reduction and can even increase the drag.

In this work, improved simplified and highly stable lattice Boltzmann methods (SHSLBMs) are developed for incompressible flows. The SHSLBM is a newly developed scheme within the lattice Boltzmann method (LBM) framework, which utilizes the fractional step technology to resolve the governing equations recovered from lattice Boltzmann equation (LBE) and reconstructs the equations in the Lattice Boltzmann frame. By this treatment, the SHSLBM directly tracks the macroscopic variables in the evolution process rather than the distribution functions of each grid node, which greatly saves virtual memories and simplifies the implementation of physical boundary conditions. However, the Chapman–Enskog expansion analysis reveals that the SHSLBM recover the weakly compressible Navier–Stokes equations with the low Mach number assumption. Therefore, the original SHSLBM can be regarded as an artificial compressible method and may cause some undesired errors. By modifying the evolution equation for the density distribution function, the improved SHSLBMs can eliminate the compressible effects. The incompressible SHSLBMs are compared with the original SHSLBM in terms of accuracy and stability by simulating several two-dimensional steady and unsteady incompressible flow problems, and the results demonstrate that the present SHSLBMs ensure the second order of accuracy and can reduce the compressible effects efficiently, especially for the incompressible flows with large pressure gradients. We then extended the present SHSLBMs to study the more complicated two-dimensional lid-driven flow and found that the present results are in good agreement with available benchmark results.