Thermally induced oscillatory rarefied gas flow inside a two-dimensional rectangular cavity is investigated based on the hybrid macro-/mesoscopic scheme. The effects of the Knudsen (Kn) numbers and the oscillation frequency of lid temperature on the flow parameters are analyzed. The Shakhov model equation is solved numerically based on the mesoscopic approach in the near-wall region, and the macroscopic approach is adopted in the bulk flow region to reduce the computational cost. To close the numerical iteration procedure, the velocity distribution functions serving as the pseudo boundary between macroscopic and mesoscopic methods are reconstructed using the high-order Hermite polynomials. Numerical simulations demonstrate that the temperature profile at the central vertical of the cavity predicted by the hybrid method is in good agreement with results from the mesoscopic method, with a maximum error of 0.23%. In addition, the computational memory cost can be saved up to about 69.91%. The hybrid approach is able to capture the nonlinear phenomenon in the thermally induced oscillatory rarefied gas flow under high Kn numbers, where the horizontal velocity no longer obeys the law of periodic oscillating cosine function, and the rise time of the horizontal velocity is much longer than the fall time. The thickness of the viscous penetration layer and the disturbed region increases as the Kn number increases and decreases as the Strouhal number increases.

This paper addresses the cruise range maximization problem for hypersonic drones by proposing a combined aerodynamic force/thrust vector trajectory optimization method. A novel continuous linear parameterization strategy for trajectory optimization is innovatively developed, achieving continuous thrust vector trajectory optimization throughout the entire flight using only 21 parameters through recursive linear function design. This approach reduces parameter dimensionality and effectively addresses sparse rewards and training difficulties in reinforcement learning. The study integrates the Deep Deterministic Policy Gradient (DDPG) algorithm with deep residual networks for trajectory optimization, systematically exploring the impact mechanisms of different aerodynamic force and thrust vector combination modes on range performance. Through collaborative trajectory optimization of thrust vectors and flight height, simulation results demonstrate that the combined trajectory optimization strategy achieves a total range enhancement of approximately 146.14 km compared to pure aerodynamic control, with continuous linearly parameterized thrust vector trajectory optimization providing superior performance over traditional segmented methods. These results verify the significant advantages of the proposed trajectory optimization approach and the effectiveness of the deep reinforcement learning framework.