A Study of Numerical Solutions of the Convection Diffusion Equation and its Applications

Abstract

The convection-diffusion equation, a key partial differential equation, models the transport of quantities such as heat or mass in various systems through convection and diffusion processes. Numerical solutions are crucial for handling its complexity, especially in higher dimensions or with intricate boundary conditions. Common numerical methods include the Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM), and Spectral Methods, each with distinct advantages and trade-offs regarding accuracy, stability, and computational cost. newline