Design exploration or optimization using computational fluid dynamics (CFD) is commonly used in the industry. Geometric variation is a key component of such design problems, especially in turbulent flow scenarios, which involves running costly simulations at every design iteration. While parametric RANS-PINN type approaches have been proven to make effective turbulent surrogates, as a means of predicting unknown Reynolds number flows for a given geometry at near real-time, geometry aware physics informed surrogates with the ability to predict varying geometries are a relatively less studied topic. A novel geometry aware parametric PINN surrogate model has been created, which can predict flow fields for NACA 4 digit airfoils in turbulent conditions, for unseen shapes as well as inlet flow conditions. A local+global approach for embedding has been proposed, where known global design parameters for an airfoil as well as local SDF values can be used as inputs to the model along with velocity inlet/Reynolds number ($\mathcal{R}_e$) to predict the flow fields. A RANS formulation of the Navier-Stokes equations with a 2-equation k-epsilon turbulence model has been used for the PDE losses, in addition to limited CFD data from 8 different NACA airfoils for training. The models have then been validated with unknown NACA airfoils at unseen Reynolds numbers.

翻译：在工业领域，基于计算流体动力学（CFD）的设计探索或优化已被广泛应用。几何变体是此类设计问题中的关键要素，尤其在湍流场景下，这通常需要在每次设计迭代中运行昂贵的仿真。虽然参数化RANS-PINN类方法已被证明能构建有效的湍流代理模型，用于在近实时条件下预测给定几何形状的未知雷诺数流动，但能够预测不同几何形状的、具有几何感知能力的物理信息代理模型仍是一个研究相对较少的课题。本文提出了一种新颖的几何感知参数化PINN代理模型，该模型能够预测湍流条件下NACA 4位数翼型在未见过的形状及入口流动条件时的流场。我们提出了一种局部+全局的嵌入方法，其中翼型的已知全局设计参数以及局部符号距离函数（SDF）值可与入口速度/雷诺数（$\mathcal{R}_e$）一同作为模型输入，以预测流场。除使用来自8种不同NACA翼型的有限CFD数据进行训练外，还采用了基于2方程k-epsilon湍流模型的Navier-Stokes方程RANS形式作为偏微分方程损失。模型随后在未知雷诺数下的未见NACA翼型上进行了验证。