Effect of Coastal Waves on Hydrodynamics in One-Inlet Coastal Nador Lagoon, Morocco

Nador lagoon is a coastal system connected to the sea through a narrow and shallow inlet; understanding its hydraulic performance is required for its design and operation. This paper investigates the hydrodynamic impacts of the whole lagoon due to tidal waves using a numerical approach. In this study we use a two-dimensional, depth-averaged hydrodynamic model based on so-called shallow water equations solved within triangular mesh by a developed efficient finite volume method. The method was calibrated and validated against observed data and applied to analyze and predict water levels, tidal currents, and wind effects within the lagoon. Two typical idealized scenarios were investigated: tide only and tide with wind forcing. The predicted sea surface elevations and current speeds have been presented during a typical tidal period and show correct physics in different scenarios

Numerical Survey of Contaminant Transport and Self-Cleansing of Water in Nador Lagoon, Morocco

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 barrier island. The case study demonstrates the potential use of modern computational hydraulics as a tool integrated in the decision support system designed to manage a lagoon ecosystem

Numerical Simulation of Dam Break Flows Using a Radial Basis Function Meshless Method with Artificial Viscosity

A simple radial basis function (RBF) meshless method is used to solve the two-dimensional shallow water equations (SWEs) for simulation of dam break flows over irregular, frictional topography involving wetting and drying. At first, we construct the RBF interpolation corresponding to space derivative operators. Next, we obtain numerical schemes to solve the SWEs, by using the gradient of the interpolant to approximate the spatial derivative of the differential equation and a third-order explicit Runge–Kutta scheme to approximate the temporal derivative of the differential equation. For the problems involving shock or discontinuity solutions, we use an artificial viscosity for shock capturing. Then, we apply our scheme for several theoretical two-dimensional numerical experiments involving dam break flows over nonuniform beds and moving wet-dry fronts over irregular bed topography. Promising results are obtained

Contribution à la modélisation des écoulements en eaux peu profondes, avec transport de polluant. (Application à la baie de Tanger)

This thesis is a contribution to the numerical solution of a hyperbolic conservation law resulting from a coupling between the Saint-Venant equations, for the modeling of flows in shallow water, and transport-diffusion equation of a non active pollutant. The mathematical model used is two dimensional, incorporating terms of friction, diffusion, surface tension and a term of variation of the bathymetry. We present a numerical model based on a higher order two-dimensional finite volume scheme , conservative and consistent, on an adaptive unstructured mesh , this model preserves the positivity of water depth and the steady state associated with the lake at rest, it can accurately capture shock waves. In a time extension to the second order is guaranteed by using a Runge-Kutta which will take into account the different speeds of propagation of information in the different issues involved. We apply the numerical model developed over several issues. Among other things, the simulation of propagation of a flood wave, flow around a singularity geometric flow on variable funds and having steep edges. And in the end, the numerical study ends with an application of the model for the simulation of pollutant transport in a real geometry with a highly variable bathymetry as like the bay of Tangier.Cette thèse est une contribution à la résolution numérique d'une loi de conservation hyperbolique résultante d'un couplage entre les équations de Saint-Venant, associée à la modélisation des écoulements en eaux peu profondes, et l'équation de transport-diffusion d'un polluant non actif. Le modèle mathématique utilisé est bi-dimensionnel, intégrant des termes de friction, de diffusion, des tensions de surface et un terme tenant compte la variation de la bathymétrie. Nous présentons un modèle numérique basé sur un schéma volumes finis bidimensionnel d'ordres deux, conservatif et consistant, sur un maillage non structuré adaptatif. Ce modèle préserve la positivité de la hauteur d'eau et l'état stationnaire associé au lac au repos, il permet de capturer avec précision les ondes de chocs. Dans le temps une extension à l'ordre deux est garantie en utilisant un schéma de Runge-Kutta ce qui permettra de prendre en compte les différentes vitesses de propagation de l'information présentes dans les différents problèmes traités. Nous appliquons le modèle numérique développé sur plusieurs problèmes. Entre autre, la simulation d'une propagation d'une onde de crue, écoulement autour d'une singularité géométrique, écoulement sur des fonds variables et présentant des fronts raides. Et en fin, L'étude numérique s'achève par une application du modèle pour la simulation du transport de polluant dans une géométrie réelle avec une bathymétrie fortement variable telle que présente la baie de Tanger

Numerical solution by meshless method of a fully-coupled bed load and shallow water flows

The one-dimensional shallow water equations (SWEs), coupled with bed load (Exner equation) were solved in this paper for the numerical simulation of the sediment transport problem. By using an efficient meshless method based on radial basis function (RBF) that approximates the unknown variables on a set of collocation nodes and Runge–Kutta fourth-order scheme to approximate the temporal derivative. Besides, the artificial viscosity to avoid oscillations, we implement the proposed numerical model of bedload and set up a series of numerical tests using various nontrivial solutions to confirm the efficiency of the suggested approaches. The numerical simulations demonstrate the accuracy, computational efficiency, and ability of the suggested numerical methods in solving the coupled Exner shallow water problem

Balanced Meshless Method for Numerical Simulation of Pollutant Transport by Shallow Water Flow over Irregular Bed: Application in the Strait of Gibraltar

This paper focuses on the implementation of an accurate meshless scheme for the simulation of the advection–diffusion of non-active pollutant in a two-dimensional depth-averaged flow. The depth-averaged flow model includes the shallow water system and the pollutant propagation described by the advection–diffusion equation with diffusion tensor. The mathematical model was implemented by using a meshless method based on local radial basis functions. This method was used to numerically evaluate the spatial derivatives and complemented with the second-order Runge–Kutta method for the time evolution. To remove the non-physical oscillations, which appear at the discontinuity, a filter based on a hyperviscosity operator was applied. To investigate the effectiveness and accuracy of the proposed scheme, a number of tests are presented, including the dam break problem, and the pure transport of a pollutant in a long channel. Finally, a hypothetical example of a pollutant transport in the Strait of Gibraltar is modeled. The results obtained are compared both with analytical solutions and with simulation results obtained by a finite volume method based on the Roe-MUSCL scheme. The main advantages of the proposed method are: (i) the simplicity of implementation, (ii) the ability to handle calculations of slowly varying flows or concentrations, as well as rapidly varying flows containing shocks or discontinuities, and (iii) the ability to satisfy the C-property and guarantee positive values of both water level and pollutant concentration

Balanced Meshless Method for Numerical Simulation of Pollutant Transport by Shallow Water Flow over Irregular Bed: Application in the Strait of Gibraltar

This paper focuses on the implementation of an accurate meshless scheme for the simulation of the advection–diffusion of non-active pollutant in a two-dimensional depth-averaged flow. The depth-averaged flow model includes the shallow water system and the pollutant propagation described by the advection–diffusion equation with diffusion tensor. The mathematical model was implemented by using a meshless method based on local radial basis functions. This method was used to numerically evaluate the spatial derivatives and complemented with the second-order Runge–Kutta method for the time evolution. To remove the non-physical oscillations, which appear at the discontinuity, a filter based on a hyperviscosity operator was applied. To investigate the effectiveness and accuracy of the proposed scheme, a number of tests are presented, including the dam break problem, and the pure transport of a pollutant in a long channel. Finally, a hypothetical example of a pollutant transport in the Strait of Gibraltar is modeled. The results obtained are compared both with analytical solutions and with simulation results obtained by a finite volume method based on the Roe-MUSCL scheme. The main advantages of the proposed method are: (i) the simplicity of implementation, (ii) the ability to handle calculations of slowly varying flows or concentrations, as well as rapidly varying flows containing shocks or discontinuities, and (iii) the ability to satisfy the C-property and guarantee positive values of both water level and pollutant concentration