Using Parametric PINNs for Predicting Internal and External Turbulent Flows

TL;DR

This work builds upon the previously proposed RANS-PINN framework and adopts a novel sampling approach that exploits the domain geometry to ensure a proper balance among the contributions from various regions within the solution domain.

Abstract

Computational fluid dynamics (CFD) solvers employing two-equation eddy viscosity models are the industry standard for simulating turbulent flows using the Reynolds-averaged Navier-Stokes (RANS) formulation. While these methods are computationally less expensive than direct numerical simulations, they can still incur significant computational costs to achieve the desired accuracy. In this context, physics-informed neural networks (PINNs) offer a promising approach for developing parametric surrogate models that leverage both existing, but limited CFD solutions and the governing differential equations to predict simulation outcomes in a computationally efficient, differentiable, and near real-time manner. In this work, we build upon the previously proposed RANS-PINN framework, which only focused on predicting flow over a cylinder. To investigate the efficacy of RANS-PINN as a viable approach to building parametric surrogate models, we investigate its accuracy in predicting relevant turbulent flow variables for both internal and external flows. To ensure training convergence with a more complex loss function, we adopt a novel sampling approach that exploits the domain geometry to ensure a proper balance among the contributions from various regions within the solution domain. The effectiveness of this framework is then demonstrated for two scenarios that represent a broad class of internal and external flow problems.

Figures (10)

• Figure 1: (a) Predicted and true values for primary variables and the corresponding (b) relative errors for flow over an airfoil.
• Figure 2: (a) Predicted and true values for primary variables and the corresponding (b) relative errors for flow over a backward-facing step.
• Figure 3: Overall RANS-PINN framework for learning surrogates to predict turbulent flow. Left panel shows the warm-up stage, with data losses. Right panel shows the second stage with PDE+data losses and individual PDE loss weights.
• Figure 4: Example of the evolution of training losses for PDE components vs epochs. The dark background represents the pre-training stage, where the pde residuals are seen to be 0 in the bottom four plots.
• Figure 5: Point cloud derived from the full CFD mesh for the three geometries, showing sampling zones.