Solvability of a supercritical free surface flow problem under gravity-capillarity

Foukroun, N.; Ait-Yahia-Djouadi, R.; Hernane-Boukari, D.

doi:10.1080/00036811.2017.1335395

Cited by 2 publications

(1 citation statement)

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“…Many other authors have studied the free surface flow problem over an obstacle, we can see [7,8,10]. In [5], the authors have considered the same problem when both effects of the gravity and of the superficial tension are taken into account. In this work, we consider a free surface flow over an obstacle placed on a flat bottom of a channel.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of a free surface flow problem over an obstacle

Beyoud

Boukari-Hernane

2019

Publ Inst Math (Belgr)

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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.

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