IndustrialMinimizer.com

I made the following derivation of the two-dimensional (2D) Burgers equation, which is a non-linear model of the convection-diffusion process.

The discretized derivation is done using the second-order central difference (CD) for the spatial derivatives, and Crank-Nicolson (CN) for the time advancement. CN method combine the stability of an implicit method with the accuracy of a method that is second-order both in space and in time, and is achieved by averaging explicit FTCS (Forward-Time-Centered-Space) and implicit BTCS (Backward in Time, Centered in Space) schemes.