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A 2d SWE - Linear Gravity Wave

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  1. Aug 24, 2016 #1
    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 [math]h[/math] 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. jcsd
  3. Aug 29, 2016 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
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