Numerical Solution of Unsteady Advection Dispersion Equation Matlab Question

I’m working on a numerical analysis discussion question and need guidance to help me learn.

Assume you have a 20m×50m rectangular pond. A pollutant enters a 1m×1m rectangular section at the center of pond and initially has the solute concentration of 1000[ML-3], while the solute concentration at other sections of this pond is zero.

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At the boundaries the concentration of the pollutant will remain zero. Following the advection dispersion formula stated below:

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?C?2C?2C

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?t = Dx ?x2 + Dy ?y2

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where Dx and Dy are constant dispersion coefficients, Dx = 1.0, Dy = 0.2, evaluate and demonstrate using appropriate mathematical tools and graphs how the solute concentration varies in time and how the pollutant is dispersed in this pond.

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For solving the above equation use the following numerical discretization methods: 1- Explicit method

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2- Crank–Nicolson method

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2-1- use Matrix technique for solving your system of linear equations.

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2-2- use an iterative technique (e.g. Gauss-Seidel method) for solving your system of linear equations.