AIMS Mathematics, 2019, 4(2): 316-326. doi: 10.3934/math.2019.2.316

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Free surface flows over a successive obstacles with surface tension and gravity effects

1 Department of Mathematics, Biskra University, Biskra, Algeria
2 Department of Mathematics, M’sila University, M’sila, Algeria

The problem of steady two-dimensional flow of a fluid of finite depth over a successive obstacles is considered. Both gravity and surface tension are taken into account in the dynamic boundary conditions. The fluid is assumed to be inviscid, incompressible and the flow to be irrotational. The flow is characterized by the two parameters, the Froude number Fr and the inverse Weber number δ. The fully non-linear problem is solved numerically by using the boundary integral equation technique. The numerical solutions for sub-critical (Fr < 1) and supercritical (Fr > 1) are presented for various values of Fr and δ. The effects of surface tension and gravity on the shape of the free surface are discussed, and solution diagrams for all flow regimes are presented.
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