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I'm using CFD (Computational fluid dynamics) to solve numerically the shallow water equations.

I'm writing a code based on roe solver, I'm supossed to get two vectors of solutions: one for the water depth ($h$) and the other one for the discharge ($hu$)...But when I compare the numerical solution with the analytical one, it comes that the water depth doesn't match, while the discharge it does match. Is there any way that I could have an error with the implementation if I'm able to get one of the two solutions?

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    For introduction to Roe solver see (https://perswww.kuleuven.be/~u0016541/Talks/roe.pdf). – 2017-01-30
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    Potentially interesting, but it would be much better to write the PDE problem using [mathjax](https://math.meta.stackexchange.com/q/5020/418542), as well as the numerical method. Then, showing curves where the numerical solution is superposed to the analytical solution could help. – 2018-01-26

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