A physics-informed neural networks modeling with coupled fluid flow and heat transfer – Revisit of natural convection in cavity

The physics-informed neural networks (PINNs) method offers a mesh-free approach for solving partial differential equations, converting the task into an optimization problem based on loss functions. By utilizing the physical governing equations, this study explores the development of a physics-driven PINNs model in solving coupled fluid flow and heat transfer problems. This approach eliminates the need for additional simulation or experimental training data, so it obviates the extra effort and computational cost associated with generating training data. The methodology is exemplified through the analysis of natural convection in a confined cavity, a challenging benchmark problem for coupled fluid flow and heat transfer scenarios. Moreover, the study examines key aspects of the PINNs, including the hyperparameter performance, convergence and accuracy analysis. We investigate in detail the accuracy and convergence behavior concerning variables such as the collocation point size, neural network size, loss functions, optimizers, network architecture, and activation functions. This comprehensive analysis aims to emphasize the importance of achieving higher predictive accuracy, which contributes significantly to enhancing the performance of the physics-driven PINNs model in predicting coupled fluid flow and heat transfer problems. Remarkably, the study introduces a novel technique to improve prediction accuracy without the need for sampling more points, consequently reducing computational costs. This is achieved through the integration of high-resolution regions within the domain. PINNs demonstrate promising performance, accurately capturing complex interactions between fluid flow and heat transfer. Further improvements are also observed when coupling the model with nondimensionalized governing equations and introducing a continuous weighting scheme for boundary loss functions to avoid sharp discontinuities at corners. It is also observed that at high Rayleigh numbers with significant gradients, variations in the efficacy of the training procedure may occur between different simulation runs due to the random generation of collocation points if an insufficient number of samples are used.