振荡稀薄气体流动的伴随形状优化
Adjoint shape optimization of oscillatory rarefied gas flows
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中文总结 AI 辅助
本文针对振动微机电系统多尺度气体流动减阻问题，提出快速收敛且渐近保形的伴随形状优化方法，经数值模拟验证其具备优异减阻性能，可高效用于相关系统设计。
中文摘要 AI 辅助
本文针对振动微机电系统中多尺度气体流动的减阻问题，提出了一种快速收敛且渐近保形的伴随形状优化方法。通过宏观合成方程加速玻尔兹曼动力学方程的收敛，其本构关系整合了连续极限项与高阶动力学修正项，以准确表征时空稀薄效应，因此该方法在保持近连续极限一致性的同时，在稀薄流动区域仍具备高动力学精度。在无限域中开展的傅里叶稳定性分析表明，该方法的谱半径低于0.5，意味着每次迭代后与收敛解的数值偏差会减半。针对振荡圆柱和梳状谐振器开展了数值模拟，结果验证了所推导的伴随灵敏度的高精度，以及该方法在不同克努森数和斯特劳哈尔数下的优异减阻性能。与传统动力学迭代方法相比，该方法可在数十次迭代内生成收敛的原始解和伴随解，且具备渐近保形特性，允许空间网格尺寸远大于分子平均自由程，从而便于高效设计振动微机电系统。
英文摘要
A fast-converging and asymptotic-preserving adjoint shape optimization method is proposed for drag reduction of multiscale gas flows in vibrating micro-electro-mechanical systems. The convergence of the Boltzmann kinetic equation is accelerated by macroscopic synthetic equations, whose constitutive relations integrate continuum-limit terms and high-order kinetic corrections to faithfully characterize spatiotemporal rarefaction effects. As such, this method maintains near-continuum limit consistency while retaining high kinetic accuracy in rarefied flow regimes. Fourier stability analysis performed in an infinite domain demonstrates that the present method yields a spectral radius below 0.5, indicating that the numerical deviation from the converged solution is halved per iteration. Numerical simulations are conducted on an oscillating cylinder and a comb-shaped resonator. The results verify the high accuracy of the derived adjoint sensitivities and the excellent drag reduction performance of the proposed method across various Knudsen and Strouhal numbers. Compared with conventional kinetic iteration methods, the present method produces convergent primal and adjoint solutions within dozens of iterations and features asymptotic preserving behavior, permitting spatial cell sizes far larger than the molecular mean free path. This facilitates efficient design of vibrating micro-electro-mechanical systems.
