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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# A 2d SWE - Linear Gravity Wave

Tags:

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**