AI 中文总结
该研究提出人工可压缩性物理信息神经网络（AC-PINN），通过松弛不可压纳维-斯托克斯方程的无散度约束，在泰勒-格林涡和Re=100圆柱尾流上验证了其有效性，同化传感器数据可恢复非定常涡街及涡脱频率。
AI 中文摘要
我们研究一种用于非定常二维不可压纳维-斯托克斯方程的物理信息神经网络（PINN），其中刚性的无散度约束被由单个标量参数ε控制的人工可压缩性（AC）松弛替代。该松弛重新引入了压力时间导数，将微分代数约束转换为PINN可直接最小化的普通残差。在具有闭式非定常解的泰勒-格林涡上，我们量化了ε的影响：残差散度与ε|∂_t p|成比例，因此更大的ε会同时提高散度和速度误差，且随着ε减小，两者单调降低并趋于饱和。在雷诺数Re=100的圆柱尾流上，普通正向AC-PINN会坍缩为定常对称分支，无法重现冯·卡门涡街；从边界层分辨的有限元参考数据中同化数百个稀疏速度传感器（我们通过分辨分离剪切层，使其斯特劳哈尔数0.176接近文献范围0.164–0.172，尽管仍略高于该范围），可在尾流中恢复非定常涡街至7%的精度，且其涡脱频率与同一参考数据的偏差在3%以内——该精度边界由参考数据自身的保真度决定，而非针对真实流场的独立验证。
英文摘要
We study a physics-informed neural network (PINN) for the unsteady, two-dimensional incompressible Navier--Stokes equations in which the stiff divergence-free constraint is replaced by an artificial-compressibility (AC) relaxation governed by a single scalar parameter $\eps$. The relaxation reintroduces a pressure time derivative, converting a differential-algebraic constraint into an ordinary residual that a PINN can minimise directly. On the Taylor--Green vortex, which admits a closed-form unsteady solution, we quantify the effect of $\eps$: the residual divergence scales as $\eps\,|\partial_t p|$, so larger $\eps$ raises both the divergence and the velocity error, and both decrease monotonically and saturate as $\eps$ is reduced. On the $Re=100$ cylinder wake the plain forward AC-PINN collapses to the steady symmetric branch and does not reproduce von Kármán shedding; assimilating a few hundred sparse velocity sensors from a boundary-layer-resolved finite-element reference (whose Strouhal number, $0.176$, we bring close to the $0.164$--$0.172$ literature band by resolving the separating shear layer, though it remains just above it) recovers the unsteady vortex street to $7\%$ over the wake and its shedding frequency to within $3\%$ of that same reference --- a bound set by the reference's own fidelity rather than an independent validation against the true flow.
Comments13 pagesö 5 figures. Original research article
