带激波流动灵敏度计算的信息几何正则化方法
Information geometric regularization for computing sensitivities of flows with shocks
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中文总结 AI 辅助
本研究针对带激波流动灵敏度计算的长期问题，推导周期边界条件下信息几何正则化（IGR）系统的正、伴随灵敏度，证明其在网格加密时收敛于有限差分或自动微分结果。
中文摘要 AI 辅助
计算带激波流动的（伴随）灵敏度是计算流体动力学中的一个长期存在的问题。激波传感器和限制器产生的虚假灵敏度常迫使从业者接受“冻结”限制器和激波传感器所带来的误差。近期提出的信息几何正则化（IGR）是一种基于偏微分方程的无粘正则化方法，用于可压缩欧拉方程，它用光滑剖面替代激波且不会衰减精细结构。本研究推导了周期边界条件下IGR系统的正向和伴随灵敏度，并证明在网格加密时，其收敛到通过有限差分或正向求解的自动微分得到的灵敏度。
英文摘要
Computing (adjoint) sensitivities of flows with shocks is a longstanding problem in computational fluid dynamics. The spurious sensitivities due to shock sensors and limiters frequently force practitioners to accept the errors incurred by "freezing" limiters and shock sensors. The recently proposed information geometric regularization (IGR) is an inviscid, PDE-based regularization of the compressible Euler equations that replaces shocks with smooth profiles without damping fine-scale structures. This work derives the forward and adjoint sensitivities for the IGR system with periodic boundary conditions and demonstrates their convergence, under grid refinement, to the sensitivities obtained by finite differences or automatic differentiation through the forward solve.
