Using Parametric PINNs for Predicting Internal and External Turbulent Flows

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.

RANS-PINN based Simulation Surrogates for Predicting Turbulent Flows

Physics-informed neural networks (PINNs) provide a framework to build surrogate models for dynamical systems governed by differential equations. During the learning process, PINNs incorporate a physics-based regularization term within the loss function to enhance generalization performance. Since simulating dynamics controlled by partial differential equations (PDEs) can be computationally expensive, PINNs have gained popularity in learning parametric surrogates for fluid flow problems governed by Navier-Stokes equations. In this work, we introduce RANS-PINN, a modified PINN framework, to predict flow fields (i.e., velocity and pressure) in high Reynolds number turbulent flow regime. To account for the additional complexity introduced by turbulence, RANS-PINN employs a 2-equation eddy viscosity model based on a Reynolds-averaged Navier-Stokes (RANS) formulation. Furthermore, we adopt a novel training approach that ensures effective initialization and balance among the various components of the loss function. The effectiveness of RANS-PINN framework is then demonstrated using a parametric PINN.