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How to implement a rigid lid aproximation for a 2d flow?

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Old   August 1, 2018, 14:40
Question How to implement a rigid lid aproximation for a 2d flow?
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I'm using a FV code to solve the shallow water equations. For certain test case, the theoretical solution was developed using a "rigid lid assumption".

However, I'm not sure on how to implement this assumtion for the SWE. Does the rigid lid assumption mean that the water surface does not change, I mean, at any time, regardless of the velocity field, the water depth will be the same?
If so, is it correct to implement the solver and just at the end simply not update the water depth and only update the momentum quantity? or should I do some change in the equations in order to implement the rigid lid assumption?
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finite volume method, shallow flows, shallow water equations, two dimensional model

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