Geometry-aware PINNs for Turbulent Flow Prediction

TL;DR

This work tackles the challenge of predicting turbulent flow around varying geometries at unseen Reynolds numbers using a geometry-aware PINN surrogate. It introduces SDF-based geometry embedding combined with a RANS formulation and a 2-equation $k$-$\epsilon$ turbulence model, evaluating three input schemes: L, G, and L+G. Using CFD data from eight NACA airfoils and six inlet velocities across a Reynolds range of $\mathcal{R}_e\in [200k,700k]$, the authors show that the L model with SDF geometry input yields the most accurate velocity and pressure fields for unseen geometries, while the G model can produce phantom boundary shapes; L+G offers a balance and competitive performance in some cases. Overall, geometry-aware PINNs demonstrate potential for near-real-time, design-iteration surrogate modeling in turbulent flows, enabling efficient exploration across shapes and flow conditions.

Abstract

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.

Figures (4)

• Figure 1: Architecture Diagram.
• Figure 2: Velocity predictions for various NACA airfoils at different $\mathcal{R}e$.
• Figure 3: Pressure predictions for various NACA airfoils at different $\mathcal{R}e$.
• Figure 4: Prediction comparison of speed for L model and G model.