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In this paper, we propose time filter algorithm based on the Backward Euler method for the non‐stationary Navier‐Stokes/Darcy problems. The decoupling method is composed of Backward Euler method and normal time filter. Stability and the second‐order convergence are also proved in details. Finally, numerical examples are listed to validate the theoretical analysis.

Energy is an important material that promotes social development and maintains human life. Clean energy has become a scientific research theme of open world which appeal to many scientists to research it. This paper inspired by the experience of sunflower growth. So we proposed a mathematical model for automatic adjustment of the maximum luminous flux for a limited solar panel, which can help to adjust the best light position. The physical model added to the light detector in the practical application, real-time comparison of the difference in illumination at different positions to adjust the direction of solar panel, thereby enhancing the utilization of light energy. In addition, in order to save space and prevent severe weather attacks, we designed a autofolding circle disc and retractable rectangular solar panels. The intelligent system judgement and decision making based on the electrical signals fed back by the wind sensor or the vibration sensor. When the wind speed reaches the threshold, it can be folded or contracted automatically, reducing manual maintenance. The fully automatic solar panels are designed in this paper, the research results show that theis model has a high utilization, strong sensitivity, safety and durability, and easy control. This is also a process of theoretical exploration of interdisciplinary services for the energy system.