Imad el Mahi

National School of Applied Sciences Oujda | ENSAO · Applied Mathematics and Mechanics

This study presents a new well-balanced scheme for solving hyperbolic conservation equations in multiple spatial dimensions on unstructured meshes. This scheme is fast, accurate, and does not require the solution of the Riemann problem during the computational process. It consists of a predictor and corrector steps: the predictor step uses the meth...

The fluid flow transport and hydrodynamic problems often take the form of hyperbolic systems of conservation laws. In this work we will present a new scheme of finite volume methods for solving these evolution equations. It is a family of finite volume Eulerian-Lagrangian methods for the solution of non-linear problems in two space dimensions on un...

The fluid flow transport and hydrodynamic problems often take the form of hyperbolic systems of conservation laws. In this work we will present a new scheme of finite volume methods for solving these evolution equations. It is a family of finite volume Eulerian–Lagrangian methods for the solution of non-linear problems in two space dimensions on un...

We present a finite volume model for the simulation of floods in urban areas. The model consists of the two-dimensional shallow water equations with variable horizontal porosity which is introduced in order to reflect the effects of obstructions. An extra porosity source term appears in the momentum equations. The main advantage of this model is th...

In river hydraulic, the classical shallow water equations are governed by the Saint-Venant system, are widely used to model water flow in rivers, lakes, reservoirs, coastal areas. As their solutions are typically non-smooth and even discontinuous, among all techniques numerical, the finite volume schemes are well suited to problems conservative, hy...

A simple unstructured finite volume scheme is used to solve the two-dimensional shallow water equations (SWEs) for simulation of dam break flows over irregular beds involving wet and dry interfaces. In space, we construct a balancing higher order upwind scheme on unstructured triangular mesh to approximate the convective and source term due to bed...

Canals and sewers are part of the structure of our cities. Flow modelling in these channels allows us to prevent and anticipate most problems and disasters that may occur. This work focuses on the modelisation of flows in open channels with variable beds and geometries. The section is rectangular or trapezoidal, variable in the direction of the len...

The intrinsic cleaning capacity of semi-enclosed hydrodynamic basins can be controlled by the time spent by each water particle inside it, giving an idea of the efficiency of this cleaning process. However, the determination of water residence time, and/or water exposure time, is thus of major interest in the environ- mental management. In this pap...

In this paper, we study the numerical approximation of bedload sediment transport due to shallow layer flows in open channels. The hydrodynamical component is modeled by a two dimensional shallow water system and the morphodynamical component by a solid transport discharge formula that depends on the hydrodynamical variables. The coupled system can...

In this paper, three depth-averaged 2-D turbulence models of Shallow Water Flows, Including the depth-averaged parabolic eddy viscosity model, modified mixing length model and standard k-Ɛ turbulence model have been confronted. We consider in this work a finite volume Non-Homogeneous Riemann Solver (SRNH) for solving the turbulence shallow water eq...

We consider in this work an expanded finite volume numerical approximation of the turbulent k   shallow water equations, on unstructured meshes, we use a simple discretization in wish only physical fluxes and averaged states are used in their formulations. To control the local diffusion in the scheme and also to preserve monotonicity, a parameter...

We consider in this work an expanded finite volume numerical approximation of the turbulent k   shallow water equations, on unstructured meshes, we use a simple discretization in wish only physical fluxes and averaged states are used in their formulations. To control the local diffusion in the scheme and also to preserve monotonicity, a par...

We present a numerical solution of the two-layer shallow water equations in two space dimensions, based on a discontinuous Galerkin finite element method. The continuous equations are discretized and solved locally using the finite element method of an unstructured computational domain using nodal polynomial basis functions of arbitrary order in sp...

The purpose of the current research is to develop an accurate and efficient solver for shallow water flows in porous media. The hydraulics is modeled by the two-dimensional shallow water flows with variable horizontal porosity. The variation of porosity in the water flows can be attributed to the variation of bed properties of the water system. As...

In this work, a Reynolds Averaged Navier-Stokes (RANS) model is adopted in a finite volume method for the numerical computation of turbulent shallow water flows on unstructured meshes. The governing equations are those of 2D Saint-Venant, they include the slope variations, the friction terms and the eddy viscosity. The effects of turbulence are inc...

We present a numerical solution of the two-layer shallow water equations in two space dimensions, based on a discontinuous Galerkin finite element method. The continuous equations are discretized and solved locally using the finite element method of an unstructured computational domain using nodal polynomial basis functions of arbitrary order in sp...

Numerical simulations are presented of the flow hydrodynamics and hypothetical contaminant dispersion patterns in Nador Lagoon, a shallow lagoon with a barrier island situated on the coast of Morocco. It is found that the natural circulation forced by the tidal flow in the lagoon is greatly affected by the development of an artificial inlet in the...

We present a robust finite volume method for large-eddy simulation of shallow water flows. The governing equations are derived from the Navier-Stokes equations with assumptions of shallow water flows including bed frictions and eddy viscosity. The turbulence effects are incorporated in the system by considering the Smagorinsky model. The numerical...

Numerical simulation of morphodynamic problems is considered. The physical model is based on the shallow-water equations coupled with the Exner equation closed by the Grass model to describe the time evolution of the bed profile. The SRNH predictor–corrector scheme and a modified Roe scheme for non-conservative systems of equations are considered f...

Comprendre la dynamique spatio-temporelle du transport-disperssion d'un contaminant reste un outil essentiel pour la prévision précise de ces impacts sur l'écologie des rivières et des zones côtières, ainsi que, pour établir des stratégies efficaces pour le contrôle de la pollution et la protection de l'environnement. L'écoulement du fluide, dans c...

A balanced adaptive scheme is proposed for the numerical solution of the coupled non-linear shallow water equations and depth-averaged advection-diffusion pollutant transport equation. The scheme uses the Roe approximate Riemann solver with centred discretization for advection terms and the Vazquez scheme for source terms. It is designed to handle...

A finite volume solver is developed for the simulation of the hydrodynamic and water recirculation in the Nador lagoon. The physical model is based on the 2D shallow water equations that include slope variations and friction losses. The convective fluxes are approximated with a Non Homogeneous Riemann Solver (SRNH) on unstructured meshes, whereas a...

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...

We present a numerical method for solving the sediment transport in the Nador lagoon. The lagoon is located on the Moroccan eastern coast and exchanges water flow with the Mediterranean sea. The governing equations consist of the well-established shallow water system including bathymetric forces, friction terms, coriolis and eddy-diffusion stresses...

The numerical simulation of sediment transport problems is considered in this paper. The physical problem is modeled through the shallow-water equations coupled with the Exner equation to describe the time evolution of the bed profile. The spatial discretization of the governing equations is carried out by a finite-volume method and a modified Roe...

The numerical simulation of sediment transport problems is considered. The physical problem is modeled through the shallow-water equations coupled with the Exner equation to describe the time evolution of the bed profile. Different models of solid transport discharge of increasing complexity are considered. The spatial discretisation of the governi...

This work concerns the numerical simulation of flow and transport of pollutants in the Nador lagoon. This is a unique ecosystem on the Moroccan coast; it presents an ecological, biological and socioeconomic interest. However, it is threatened by discharges from industrial and agricultural untreated activities. The flow and transport of pollutants i...

Unstructured finite volume methods are receiving increased attention mainly because of their ability to provide a flexible spatial discretization. Hence, some areas can be resolved in great detail while not over-resolving other areas. Development of these models is an ongoing process with significant longstanding issues with adaptive grids, efficie...

This work concerns the numerical simulation of free surface flows on non flat topography. This flow is described by the shallow water equations. Cell centered finite volume scheme on an unstructured mesh is used, it is coupled with an adaptive procedure based on multi-level refinement-unrefinement for spatial discretization, and a two steps Runge K...

Two-dimensional dam-break hydraulics over erodible sediment beds are solved using a well-balanced finite volume method. The governing equations consist 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...

A numerical comparison is presented between a meshless method and a finite volume method for solving the shallow water equations. The meshless method uses the multiquadric radial basis functions whereas a modified Roe reconstruction is used in the finite volume method. The obtained results using both methods are compared to experimental measurement...

A numerical algorithm based on a Non Homogeneous Riemann solver is developed to compute contaminant transport in the Nador lagoon. A new formulation of the discretisation of the bed slope source terms is proposed. The scheme is well balanced, can be applied to model flows on complicated geometries using unstrutured meshes and conserves the positivi...

Two explicit numerical schemes, Lax-Wendroff Richtmyer in finite element and Roe in finite volume version, are applied to calculate steady, two dimensional depth averaged Saint-Venant equations with source terms. Both schemes are formally second order accurate and conditionally stable. For the Roe scheme, the second order in space is reached by a M...

The simulation of sediment transport, based on the shallow-water equations coupled with Grass model for the sediment transport equation is considered. for the morphodynamic, namely the Exner equation and the . The aim of the present paper is to investigate the behavior of implicit linearized schemes in this context. The equations are discretized in...

The numerical simulation of sediment transport problems is considered.The problem is modeled through the shallow-water equations coupled with the Exner equation to describe the time evolution of the bed prole. The Grass model is used for the sediment transport. The governing equations arediscretized by using two different finite-volume methods, the...

In this paper a finite volume algorithm based on Non Homogeneous Riemann solver is used to solve the equations governing the shallow water flow coupled with the transport-diffusion of a pollutant. The variation of bathymetry, frictions due to roughness of the bottom and wind effects are taken into account in the model. The scheme is used on unstruc...

We present a new finite volume method for flux-gradient and source-term balancing in the numerical solution of shallow water equations on nonflat topography. The method consists of a predictor stage for discretization of gradient terms and a corrector stage for treatment of source terms. The numerical fluxes at the interfaces of each triangle are r...

This work concerns the numerical simulation of free flow on irregular bed. This flow can be described by the shallow water or Saint-Venant equations, written in conservative form. The numerical approximation model is based on non structured finite volume method coupled with dynamical adaptive mesh for spatial discretisation and a second order TVD R...

An adaptive finite volume method is proposed for the numerical solution of pollutant transport by water flows. The shallow water equations with eddy viscosity, bottom friction forces and wind shear stresses are used for modelling the water flow whereas, a transport-diffusion equation is used for modelling the advection and dispersion of pollutant c...

This paper presents details of finite volume and finite element numerical models based on unstructured triangular meshes that are used to solve the two-dimensional nonlinear shallow water equations (SWEs). The finite volume scheme uses Roe's approximate Riemann solver to evaluate the convection terms. Second order accuracy is achieved by means of t...

A finite-volume method on unstructured grids for solving systems of conservation laws of compressible fluids is extended to chemically reacting non-equilibrium flow problems at very low Mach numbers. Convergence and accuracy is ensured by local preconditioning, generalised to reactive multi-species flows and incorporated in a flux difference formul...

Pollutant transport by shallow water flows on non-flat topography is presented and numerically solved using a finite volume scheme. The method uses unstructured meshes, incorporates upwinded numerical fluxes and slope limiters to provide sharp resolution of steep bathymetric gradients that may form in the approximate solution. The scheme is non-osc...

Les équations de Saint Venant bidimensionnelles sont résolues par deux méthodes différentes. La première, centrée, est de type éléments finis. La seconde, décentrée, est de type volumes finis. Toutes les deux sont de second ordre dans le temps et dans l'espace. La validité des deux méthodes est démontrée sur des tests numériques et les performances...

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...

In this paper, hydrogeological and geophysical data are used to validate a numerical model developed to predict seawater intrusion into coastal aquifers. The cell-centered finite volume method is adopted here to solve the set of coupled partial differential equations describing the motion of saltwater and freshwater separated by a sharp interface....

The aim of this paper is to reconstruct a simple and accurate numerical method for predicting dispersion of contaminants in the Strait of Gibraltar. Shallow water equations with eddy viscosity and slop stress forces are used for modelling the free-surface flow while, an advection-diffusion equation is employed for the dispersion of contaminants. Th...

The motion of flood waves resulting from dam break are investigated numerically. The Roe approximate Riemann solver is applied to the system of shallow water equations. This system is combined with pollutant transport diffusion equation and solved on structured and non-structured grids. An entropy fix for the numerical scheme enables to handle init...

The motion of flood waves resulting from dam break are investigated numerically. The Roe approximate Riemann solver is applied to the system of shallow water equations. This system is combined with pollutant transport diffusion equation and solved on structured and non-structured grids. An entropy fix for the numerical scheme enables to handle init...

This work deals with the numerical simulation on an unstructured mesh of the ignition and burning of an isolated fuel droplet modelled as a porous cylindrical wall. The reaction is assumed to be described by the equation A + B → P. The complexity of the physical model considered, including multi-scale feature and the presence of stiff propagating f...

A numerical methodology for the simulation of sediment transport is consid-ered. The model is based on the shallow-water equations coupled with a sediment transport equation for the morphodynamic, namely the Exner equation and the Grass model. The aim of the present paper is to investigate the behavior of implicit linearized schemes in this context...

We propose a numerical model for predicting sea-surface temperature distribution in the Strait of Gibraltar. The model is derived from the vertically integrated incompressible Navier-Stokes equations involving a hydrostatic pressure and a density variation according to the Boussinesq approximation. The distribution of sea-surface temperature is mod...