2d SWE -- CFD Online Discussion Forums

August 24, 2016, 07:04	2d SWE	#1
FrancescoLRomeo New Member Francesco L. Romeo Join Date: Jun 2016 Location: Milan, Italy Posts: 6 Rep Power: 9	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 , with initial velocity field and an initial Gaussian perturbation of the free surface elevation 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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