Computing two dimensional flood wave propagation using unstructured finite volume method: applications to the Ourika valley. (English) Zbl 1490.76140
Summary: This study is devoted to the flood wave propagation modellingfl corresponding to a realistic situation. The equations that governs the propagation of a flood wave, in natural rivers, corresponds to the free surface flow equations in the Shallow Water case. The obtained two dimensional system, known as Saint Venant’s system, is derived from the three-dimensional incompressible Navier Stokes equations by depth-averaging of the state variables. This system is written in a conservative form with hyperbolic homogeneous part. The discretization of the convection part is carried out by the use of the finite volume method on unstructured mesh. To increase the accuracy of the scheme, the MUSCL technique is used. The diffusive part is discretized using a Green-Gauss interpolation technique based on a diamond shaped co-volume. For the numerical experiment, we have studied a realistic channel of the Ourika valley which is located in Morocco. The flood occurred on August 1995 is simulated with the objective of evaluating the behavior of the wave propagation in the channel. The results of the proposed numerical model gives velocities and free surface elevations at different stopped times of the simulation.
MSC:
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
| 35L65 | Hyperbolic conservation laws |
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
| 76N15 | Gas dynamics (general theory) |
Keywords:
shallow water equations; unstructured mesh; Roe scheme; Green-Gauss interpolation; finite volume method; Manning equation; flood; Ourika valleyReferences:
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