Numerical Flux

Numerical flux calculation is crucial for accurately solving partial differential equations (PDEs) in various fields, particularly fluid dynamics, where it represents the flow of conserved quantities across computational boundaries. Current research focuses on improving flux calculations, particularly in handling shocks and discontinuities, using advanced techniques like machine learning (ML) and deep learning (DL), including neural operators (e.g., Fourier Neural Operators) and generative adversarial networks (GANs). These methods aim to enhance accuracy, efficiency, and robustness compared to traditional numerical schemes, with applications ranging from weather prediction to plasma physics simulations and groundwater modeling.