Physics-Informed Neural Network with Turbulent Flow over Fluid Saturated Porous Media
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The implementation of turbulent composite porous-fluid systems has gained widespread significance due to their versatile applications across various engineering domains. A key factor influencing porous flow is the intricate interplay between momentum and energy within both porous and non-porous zones. Numerical methods, encompassing both volume-averaged and pore-scale simulations to solve partial differential equations, are commonly employed to investigate the dynamics of flow in porous media. However, these conventional techniques exhibit inherent limitations [1]. With the advent of deep learning in engineering, the Physics-Informed Neural Network (PINN) has garnered considerable attention for its unique ability to integrate governing physical equations into the neural network training process, establishing itself as a powerful tool for solving diverse engineering problems [2]. Recent studies have demonstrated promising results for PINN predictions in laminar and turbulent flows with heat transfer in simple geometries, suggesting its applicability beyond current numerical methods. Nevertheless, challenges persist in addressing the complex fluid movement in porous media with intricate geometries using PINN. To overcome this challenge, we incorporate the k-ε turbulence model into the Physics-Informed Neural Network. Additionally, domain decomposition between porous and non-porous regions was leveraged to enhance prediction accuracy while minimizing reliance on extensive training datasets. In training the PINN model with diverse datasets within the training domain, turbulent flow is inadequately reconstructed in predictions. The presence of complex geometry in pore-scale simulations makes it challenging for the neural network to converge to a global minimum of the loss function and yield accurate solutions. However, employing domain decomposition with a sparse dataset within the training domain significantly improves flow reconstruction. The resulting predictions from the PINN model exhibit better agreement with reference Reynolds-Averaged Navier-Stokes (RANS) data, as illustrated in Figure 1. This study demonstrates the successful implementation of the k-ε turbulence model in PINN training, particularly when utilizing a sparse dataset. Furthermore, domain decomposition based on flow complexity criteria facilitates easier training of the PINN, leading to more accurate and precise results.