What are the numerical methods used for solving shallow water equations (PDEs) with a mass source, at the synoptic scales of the atmosphere, if I have a finite east-west boundary (may be periodic wave solutions)? What are the limitations of the methods?

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    $\begingroup$ Sounds a little bit like a homework question. Can you show us some of the work you have done so far? Maybe then you can pose a more concrete question about some of the methods you are trying to understand. $\endgroup$ May 27 '16 at 5:33
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    $\begingroup$ Your question is too broad as it is right now. Can you please include your exact equations that you aim to solve, and what are some specific problems that you encounter in solving them? $\endgroup$ May 27 '16 at 15:44

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