Hi,(adsbygoogle = window.adsbygoogle || []).push({});

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 σ_{x}^{2})] exp [- (y - L/2)^2 / (2 σ_{y}^{2}) ]

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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# A 2d SWE - Linear Gravity Wave

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