# A 2d SWE - Linear Gravity Wave

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1. Aug 24, 2016

### Keccogrin

Hi,
I have some questions about the 2D SWE (Shallow Water Equations).
I would like to know if an exact (analytical) solution is available in the case of the (linear) surface "gravity" wave.
Indeed, my example of interest is given by a square [0,L]2 with initial velocity field u = v = 0 and an initial Gaussian perturbation of the free surface elevation $h$ placed in the center of the domain:
h(x,y,t=0) = H + η' exp [- (x - L/2)2 / (2 σx2 )] exp [- (y - L/2)^2 / (2 σy2) ]

I know that, in 1D, a simple exact solution is available, which derives from a linearization of the Sain-Venant equations.

Can you give me some references? (I am studying on Leveque, "Finite Volume methods for hyperbolic Problems" 2004)

Thank you,
Best regards,

Francesco

2. Aug 29, 2016