BCs of hyperbolic Shallow Water Equation
I am a graduate student who studies hydrodynamics. I want to solve hyperbolic 2D shallow water equations (1 continuity eq, 2 momentum eqs) by Finite Volume Method using limiter with unstructued grid. For 1D SaintVenant equation, when flow is subcritical we specify 1 boundary condition (discharge or flow velocity) at upstream end and another one(water depth) is calculated from characteristic equation at upstream end. I got to know it becomes complicated when the problem is 2D. The characeristic line is no longer expressed in 2D plane. In 2D shallow water equation the unknowns are u, v, h (u,v=x,y velocity; h=water depth). For subcritical flow two variables(u, v) are known and one variable(h) us unknown at inflow boundary. How should I determine h ?

Re: BCs of hyperbolic Shallow Water Equation
You might find the answer by looking at a few demonstration cases describing the main details of how PHOENICS , finitevolume code, has been taught to deal with Shallow Water Equations for the sub and supercritical flows to simulate:
Regards Sergei Zhubrin 
Re: BCs of hyperbolic Shallow Water Equation
Thanks for your reply. I visited PHOENICS sites that you said. But the demonstration cases also used fixed flux at inlet boundary,ie. all (3) boundary values are imposed at inlet boundary by Dirichlet type. Anyway, I greatly appreciate your answer. :)
Regards Kang, S. K. 
Re: BCs of hyperbolic Shallow Water Equation
If one introduces the terms representing the elevation of bed above arbitrary horizontal datum as a momentum sources, the depths at the inlet and outlet planes can be calculated as a part of the solution without imposing the fixed inlet fluxes.
The corresponding changes of BC are straightforward to derive and implement. Regards Sergei Zhubrin 
Re: BCs of hyperbolic Shallow Water Equation
Then, can you please send me the derivations of the terms for super and subcritical case privately.
Thanks for your reply. Regards Kang, S. K. 
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