Modeling convective heat transfer in a cavity flow using physics-informed neural networks

Physics-Informed Neural Networks (PINNs) have gained popularity across various disciplines in science and engineering, due to its capability of solving partial differential equations (PDE) with a mesh-free nature. While computational fluid dynamics (CFD) has achieved considerable success and matured into a powerful tool, recent efforts have been taken on solving the Navier-Stokes equations using novel PINNs models. This project aims to couple the energy equation to the Navier-Stokes equations, in order to accurately predict the physics of convective heat transfer in a lid-driven cavity flow. By implementing a fully-connected neural network with a wider first layer with sine as activation function and the rest layers with tanh to avoid local minima, tuning hyperparameters such as learning rate schedule, and imposing boundary hard constraints which refer to NSFnet by Jin et al. (2021). The model successfully predicts two-dimensional lid-driven cavity flow of Reynolds number up to 5000, validated against a CFD result. Solutions for mixed convection in two dimensions, where the lid-driven forcing is opposing or assisting the buoyancy-induced flow, are also attempted using the present PINNs framework. Further investigations extend the framework to analyze three-dimensional flows to model more complex physics.