Numerical solution of a free surface flow problem over an obstacle

Abstract

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.