In this work, we propose a general single-node nonslip hydrodynamic boundary condition for the lattice Boltzmann method. The construction of the boundary scheme is the combination of the bounce back rule for the nonequilibrium part of the density distribution and linear interpolation. The proposed boundary condition is very simple, universal, stable, and accurate. The asymptotic analysis of the newly proposed boundary condition confirms that is of second-order accuracy. The numerical experiments demonstrate that the boundary condition is indeed second-order accurate for both straight and curved boundaries.

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Prior literature on the green innovation effects of green credit policies is extensive. However, few scholars have focused on the impact of green credit policies on the high-quality development of heavily-polluting enterprises. Based on this, this study employs the difference-in-differences (DID) model to explore the causal relationship between the Green Credit Guidelines (Guidelines) issued in 2012 and the high-quality development of heavily-polluting enterprises. Additionally, we test whether the effect of upgrading human resources in enterprises strengthens this causal relationship. Our findings suggest that the implementation of the Guidelines has significantly promoted the development quality of heavily-polluting enterprises and the promotion effect is more significant in enterprises with higher development quality, state-owned enterprises, large-scale enterprises, and enterprises in the western region of China. Further research reveals that the effect of upgrading human resources in enterprises has reinforced the positive impact of Guidelines on the high-quality development of enterprises. From the perspective of high-quality development of enterprises, in this paper, we expand the research into the effects of green credit policy, providing a decision-making reference for the promotion and improvement of subsequent green credit policy in the future.

The cavitation bubbles that collapse in the hydraulic machinery can cause damage to the structure and the internal wall. In order to find feasible preventive measures, the mechanism of cavitation bubble collapse needs to be thoroughly studied. However, the influence of the initial radius or the interaction between multi‐bubbles has not been studied in depth. In this paper, the collapse process of single‐ and double‐bubble system is studied by the volume of fluid (VOF) method. Three conditions are considered in this paper, single‐bubble (R0 = 0.3 mm, R0 = 0.4 mm) and double‐bubble system (R0,1 = 0.3 mm and R0,2 = 0.4 mm). The time evolution of pressure, bubble radius, radial velocity, and acceleration during the bubble collapse can be obtained. The bubble collapse time, pressure distribution, and radial velocity of single bubble are verified by theoretical values. It is found that with the increase of bubble initial radius, the collapse, and rebound time is delayed, the maximum pressure of the bubble center increases, the minimum radius of the bubble decreases, the maximum radial velocity increases. In double‐bubble system, during the first rebound of the small bubble, the central pressure, radius and radial velocity of the small bubble fluctuate with time. And the collapse time of each bubble is delayed, the maximum central pressure decreases and the minimum radius of the bubble increases.