Imad Elmahi

Bio: Imad Elmahi is an academic researcher from Entertainments National Service Association. The author has contributed to research in topics: Finite volume method & Shallow water equations. The author has an hindex of 9, co-authored 31 publications receiving 330 citations. Previous affiliations of Imad Elmahi include Institut national des sciences appliquées de Rouen.

An unstructured finite‐volume method for coupled models of suspended sediment and bed load transport in shallow‐water flows

Abstract: SUMMARY The aim of this work is to develop a well-balanced finite-volume method for the accurate numerical solution of the equations governing suspended sediment and bed load transport in two-dimensional shallow-water flows. The modelling system consists of three coupled model components: (i) the shallow-water equations for the hydrodynamical model; (ii) a transport equation for the dispersion of suspended sediments; and (iii) an Exner equation for the morphodynamics. These coupled models form a hyperbolic system of conservation laws with source terms. The proposed finite-volume method consists of a predictor stage for the discretization of gradient terms and a corrector stage for the treatment of source terms. The gradient fluxes are discretized using a modified Roe's scheme using the sign of the Jacobian matrix in the coupled system. A well-balanced discretization is used for the treatment of source terms. In this paper, we also employ an adaptive procedure in the finite-volume method by monitoring the concentration of suspended sediments in the computational domain during its transport process. The method uses unstructured meshes and incorporates upwinded numerical fluxes and slope limiters to provide sharp resolution of steep sediment concentrations and bed load gradients that may form in the approximate solutions. Details are given on the implementation of the method, and numerical results are presented for two idealized test cases, which demonstrate the accuracy and robustness of the method and its applicability in predicting dam-break flows over erodible sediment beds. The method is also applied to a sediment transport problem in the Nador lagoon.Copyright © 2013 John Wiley & Sons, Ltd.

Ignition of fuel issuing from a porous cylinder located adjacent to a heated wall: A numerical study

Abstract: This work deals with the numerical simulation on an unstructured mesh of the ignition and burning in an oxidizing atmosphere of a fuel droplet heated on one side. This is relevant for studying the ignition of droplets in a spray when they are crossing a flame zone stabilized in it. The droplet here is replaced by a porous cylinder, and the flame by a hot solid wall. The reaction is assumed to be described by a single step, A + νB → P. The cell-centred finite volume scheme considered here uses a generalized Roe's approximate Riemann solver with the monotonic upwind scheme for conservative laws (MUSCL) technique for the convective part and Green–Gauss type interpolation for the viscous part. The thinness of the reaction zone is taken into account by using an adaptive refinement–unrefinement procedure. It has been found that the process of droplet ignition takes place by means of a propagation of a triple flame around the ‘droplet’ when the chemical reaction is sufficiently fast with respect to the molecular...

Entrainment of bed material by Earth‐surface mass flows: Review and reformulation of depth‐integrated theory

Abstract: Earth-surface mass flows such as debris flows, rock avalanches, and dam-break floods can grow greatly in size and destructive potential by entraining bed material they encounter. Increasing use of depth-integrated mass and momentum conservation equations to model these erosive flows motivates a review of the underlying theory. Our review indicates that many existing models apply depth-integrated conservation principles incorrectly, leading to spurious inferences about the role of mass and momentum exchanges at flow-bed boundaries. Model discrepancies can be rectified by analyzing conservation of mass and momentum in a two-layer system consisting of amoving upper layer and static lower layer. Our analysis shows that erosion or deposition rates at the interface between layers must, in general, satisfy three jump conditions. These conditions impose constraints on valid erosion formulas, and they help determine the correct forms of depth-integrated conservation equations. Two of the three jump conditions are closely analogous to Rankine-Hugoniot conditions that describe the behavior of shocks in compressible gasses, and the third jump condition describes shear traction discontinuities that necessarily exist across eroding boundaries. Grain-fluid mixtures commonly behave as compressible materials as they undergo entrainment, because changes in bulk density occur as the mixtures mobilize and merge with an overriding flow. If no bulk density change occurs, then only the shear traction jump condition applies. Even for this special case, however, accurate formulation of depth-integrated momentum equations requires a clear distinction between boundary shear tractions that exist in the presence or absence of bed erosion.

A simple and efficient unstructured finite volume scheme for solving the shallow water equations in overland flow applications

Abstract: An edited version of this paper was published by AGU. Copyright (2015) American Geophysical Union.