- #1

Keccogrin

- 1

- 0

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 \(\displaystyle h\) 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,Francesco