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Numerical solution of a free surface flow problem over an obstacle

We consider a free surface flow problem of an incompressible and inviscid
 fluid, perturbed by a topography placed on the bottom of a channel. We
 suppose that the flow is steady, bidimensional and irrotational. We neglect
 the effects of the superficial tension but we take into account the gravity
 acceleration g. The main unknown of our problem is the equilibrium free
 surface of the flow; its determination is based on the Bernoulli equation
 which is transformed as the forced Korteweg-de Vries equation. The problem
 is solved numerically via the fourth-order Runge-Kutta method for the
 subcritical case, and the finite difference method for the supercritical
 case. The results obtained are illustrated by several figures, where the
 height h of the obstacle, and the value of the Froude number F of the flow,
 are varied. Note that different shapes of the obstacle have been considered.