Shallow water equations - finite difference integration

Dear All

Could anyone send me some simple MATLAB code to do an Arakawa-Lamb
finite difference integration of the shallow water equations? Mostly I
really need to see the scheme laid out clearly and explicitly.

Also, anyone had any luck with test cases? I've read that the shallow
water equations generate detail on arbitrary fine scales very quickly,
so that generally you need an artificial diffusion term to prevent
blow up?

Many thanks in advance,
Max

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