用于灵敏度分析的保渐近伴随统一气体动理学格式
An asymptotic-preserving adjoint unified gas kinetic scheme for sensitivity analysis
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中文总结 AI 辅助
针对多尺度气体动力学高维灵敏度分析的梯度评估难题，提出保渐近伴随统一气体动理学格式，通过双一致格式、特定投影提升方案等实现高效计算，经多类流动案例验证了其精度与鲁棒性。
中文摘要 AI 辅助
针对涵盖连续流到稀薄流区域的多尺度气体动力学的高维灵敏度分析与不确定性量化，需要计算高效且数学一致的梯度评估方法。本文基于双一致格式，开发了统一气体动理学格式（UGKS）的离散伴随方法；伴随系统直接由离散微观速度分布方程耦合宏观矩相容条件推导得到。为解决刚性跨尺度耦合问题，提出了通过宏观矩投影与微观提升构造的保渐近（AP）伴随格式，该格式可消除连续流区域中刚性碰撞耦合，去除碰撞时间步长限制。数值实现中，采用与前向UGKS单元顶点数据结构镜像的内存高效残差评估算法，绕过速度空间的内存瓶颈；此外，设计了宏观-微观预测-校正隐式推进格式，在不求解全局耦合系统的前提下加速收敛。在宽克努森数范围（包括顶盖驱动空腔热传导、微通道热蠕变流动、钝头体高超声速绕流）内，针对独立线性化UGKS求解器，严格验证了所提AP伴随格式的精度、一致性与鲁棒性。
英文摘要
High-dimensional sensitivity analysis and uncertainty quantification for multiscale gas dynamics, spanning the continuum to rarefied regimes, require computationally efficient and mathematically consistent gradient evaluation. This paper develops a discrete adjoint method for the unified gas-kinetic scheme (UGKS) based on a dual-consistent formulation. The adjoint system is derived directly from the discrete microscopic velocity-distribution equation coupled with the macroscopic-moment compatibility conditions. To resolve the stiff cross-scale coupling, we propose an asymptotic-preserving (AP) adjoint formulation constructed via macroscopic-moment projection and microscopic lifting. Under this framework, the AP adjoint formulation eliminates the stiff collision coupling and removes the collision-time step restriction in the continuum regime. Numerically, a memory-efficient residual-evaluation algorithm that mirrors the forward UGKS cell-vertex data structure is implemented to bypass the memory bottleneck in velocity space. Furthermore, a macroscopic--microscopic predictor--corrector implicit marching scheme is designed to accelerate convergence without solving a globally coupled system. The accuracy, consistency, and robustness of the proposed AP-adjoint scheme are rigorously verified against an independent linearized UGKS solver across a wide range of Knudsen numbers, including lid-driven cavity heat conduction, microchannel thermal creep flow, and hypersonic flow past a circular cylinder.
