Convection Diffusion Equation

The convection-diffusion equation describes the transport of a quantity influenced by both convection (advection) and diffusion processes, a fundamental problem across numerous scientific disciplines. Current research focuses on improving numerical solutions, particularly for challenging problems with steep gradients, using advanced techniques like Physics-Informed Neural Networks (PINNs) and their variations (e.g., densely multiplied PINNs, Lagrangian PINNs). These methods aim to enhance accuracy and efficiency, addressing limitations of traditional numerical approaches. The improved modeling of convection-diffusion phenomena has significant implications for diverse fields, including weather prediction, material science, and even linguistics, where it provides a framework for understanding the spread of linguistic features.