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Two-dimensional (2D) Burgers equation derivation

26 November, 2020 Leave a comment Go to comments

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

Burgess equation 1 - Laura Almara Burgess equation 3 - Laura Almara

Burgess equation 2 - Laura Almara Burgess equation 4 - Laura Almara

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.

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