Solving Convection Equation Using Upwind Scheme

This MATLAB implementation utilizes the upwind scheme to solve convection equations, which find extensive applications across various engineering disciplines. The program's versatility makes it suitable for studying diverse physical phenomena including weather forecasting, meteorology, fluid dynamics, and astronomy. The upwind discretization method employed provides high numerical stability and accuracy, enabling solutions to complex convection-dominated problems with minimal numerical diffusion. The implementation features key MATLAB functions for spatial discretization using first-order upwind differences and time integration through explicit schemes. Additionally, the package includes a leapfrog scheme implementation for solving initial value problems of diffusion equations, making the program more comprehensive and applicable to broader domains such as chemical reactions and physical chemistry. The code structure separates convection and diffusion solvers into modular functions, allowing users to easily adapt boundary conditions and parameters. This robust computational tool offers significant value to engineers, scientists, and researchers working with transport phenomena, providing reliable numerical solutions with clear documentation on scheme implementation and stability considerations.