The implementation of the boundary condition at the corner points is very important. The discontinuities at the corner points propagate in the computational domain and have a great impact on the surrounding points and the global solution in the evolution process, resulting in the poor precision or the unphysical oscillatory behavior. However, it had been a largely under explored domain in the discrete unified gas kinetic scheme (DUGKS) methods. In the last few years, the DUGKS is proposed as a mesoscopic finite volume method with great development potential. In order to improve accuracy and efficiency, this paper proposes a new corner boundary condition for the DUGKS, which is deduced strictly in theory and available to satisfy conservation relations. The new corner boundary condition is validated by three numerical tests: the flow past a square cylinder (external flow), lid‐driven cavity flow (internal flow) and flow past the AUV (nonright angle corner). The results show that the convergence efficiency and accuracy of the DUGKS are improved by the new corner boundary condition.

The specific objective of the present work study is to propose an anisotropic slip boundary condition for three-dimensional (3D) simulations with adjustable streamwise and spanwise slip length by the discrete unified gas kinetic scheme (DUGKS). The present boundary condition is proposed based on the assumption of nonlinear velocity profiles near the wall instead of linear velocity profiles in a unidirectional steady flow. Moreover, a 3D corner boundary condition is introduced to the DUGKS to reduce the singularities. Numerical tests validate the effectiveness of the present method, which is more accurate than the bounce-back and specular reflection slip boundary condition in the lattice Boltzmann method. It is of significance to study the lid-driven cavity flow due to its applications and its capability in exhibiting important phenomena. Then, the present work explores, for the first time, the effects of anisotropic slip on the two-sided orthogonal oscillating micro-lid-driven cavity flow by adopting the present method. This work will generate fresh insight into the effects of anisotropic slip on the 3D flow in a two-sided orthogonal oscillating micro-lid-driven cavity. Some findings are obtained: The oscillating velocity of the wall has a weaker influence on the normal velocity component than on the tangential velocity component. In most cases, large slip length has a more significant influence on velocity profiles than small slip length. Compared with pure slip in both top and bottom walls, anisotropic slip on the top wall has a greater influence on flow, increasing the 3D mixing of flow. In short, the influence of slip on the flow field depends not only on slip length but also on the relative direction of the wall motion and the slip velocity. The findings can help in better understanding the anisotropic slip effect on the unsteady microflow and the design of microdevices.

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Significant pressure fluctuation may exists at the inlet of the draft pipe during load shedding of water pump and turbine sets. When the tail-water level is low, the minimum water hammer pressure at the inlet of the draft pipe set is higher than evaporation pressure; however, the overall pressure after superposition with pulsating pressure may reach the evaporation pressure in an instant. In these cases, it is unknown if a cavity is formed or water column separation is induced. It is also unknown how frequency and amplitude of the pulsating pressure affect the formation of cavity or water column separation. However, in terms of the physical formation of water column separation, liquid pressure reaching evaporation pressure is only the necessary condition of water column separation rather than a sufficient condition because the growth and aggregation of cavitations take time. In addition, water column separation could be induced only when the cavitation rate in the water reaches a specific value and gas-liquid relative motion occurs. In this study, based on the uniform cavitation distribution model, the critical of flow velocity gradients are calculated both in front and at the back of the section and are the sufficient condition of water column separation. This study uses the criterion of when the ratio of the vaporous cavitation volume to the volume of the pipe segment with a length of Δx exceeds a critical cavitation rate for classifying water column separation segments and non-water column separation segments. In water column separation segments, a concentrated vaporous cavitation model is used for calculation; however, dynamic meshes should be applied for tracking the change of vaporous cavitations. In the non-water column separation segments, the vaporous cavitation volume can be calculated according to the continuity equation but is converted into a cavitation rate in the pipe segment and substituted into gas-liquid two-phase equation to calculate wave velocity. Next, a case study was performed on a pipe-valve system. By taking into account the pulsating pressures with different frequencies and amplitudes on the downstream side in the valve closing process, water column separation and merging processes were analyzed and the change in flows, cavitation volumes and pressures on various sections and their laws during the transient process were concluded.

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