Open AccessNumerical solution of a free surface flow problem over an obstacle
Author(s) -
Samira Beyoud,
Dahbia Boukari-Hernane
Publication year - 2019
Publication title -
publications de l'institut mathématique
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.246
H-Index - 17
eISSN - 1820-7405
pISSN - 0350-1302
DOI - 10.2298/pim1920135b
Subject(s) - froude number , inviscid flow , bernoulli's principle , conservative vector field , free surface , obstacle , flow (mathematics) , supercritical flow , mathematics , open channel flow , mechanics , potential flow , surface tension , compressibility , mathematical analysis , physics , geometry , thermodynamics , political science , law
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.