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Old   August 24, 2016, 07:04
Default 2d SWE
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Francesco L. Romeo
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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 + \eta' \exp \biggl[- \frac{ (x - L/2)^2 }{2 \sigma_x^2} \biggl] \exp \biggl[- \frac{ (y - L/2)^2 }{2 \sigma_y^2} \biggl]

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
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