6 citations · 12 across the 15 of their papers we have counts for
16 papers
Discrete positivity and maximum principles for a finite element discretization of the Richards equation
Abderrahmane Benfanich, Yves Bourgault, Abdelaziz Beljadid
Standard finite element discretizations of the Richards equation may violate the discrete minimum principle, producing unphysical negative saturations. While existing bound-preserv…
Mathematical analysis for a doubly degenerate parabolic equation: Application to the Richards equation
Abderrahmane Benfanich, Yves Bourgault, Abdelaziz Beljadid
This paper presents a mathematical analysis of a doubly degenerate parabolic equation and its application to the Richards equation using a bounded auxiliary variable. We establish…
A finite element method using a bounded auxiliary variable for solving the Richards equation
Abderrahmane Benfanich, Yves Bourgault, Abdelaziz Beljadid
The Richards equation, a nonlinear elliptic parabolic equation, is widely used to model infiltration in porous media. We develop a finite element method for solving the Richards eq…
LRBF meshless methods for predicting soil moisture distribution in root zone
Mohamed Boujoudar, Abdelaziz Beljadid, Ahmed Taik
In this paper, we first propose a coupled numerical model of unsaturated flow in soils and plant root water uptake. The Richards equation and different formulations are used in the…
Implicit EXP-RBF techniques for modeling unsaturated flow through soils with water uptake by plant roots
Mohamed Boujoudar, Abdelaziz Beljadid, Ahmed Taik
Modeling unsaturated flow through soils with water uptake by plan root has many applications in agriculture and water resources management. In this study, our aim is to develop eff…
A semi-implicit second-order temporal scheme for solving the pressure head-based form of Richards' and advection-dispersion equations
Nour-eddine Toutlini, Abdelaziz Beljadid, Azzeddine Soulaïmani
In this study, a novel semi-implicit second-order temporal scheme combined with the finite element method for space discretization is proposed to solve the coupled system of infilt…
Localized RBF methods for modeling infiltration using the Kirchhoff-transformed Richards equation
Mohamed Boujoudar, Abdelaziz Beljadid, Ahmed Taik
We develop a new approach to solve the nonlinear Richards equation based on the Kirchhoff transformation and localized radial basis function (LRBF) techniques. Our aim is to reduce…
A numerical model preserving nontrivial steady-state solutions for predicting waves run-up on coastal areas
H. Karjoun, A. Beljadid
In this study, a numerical model preserving a class of nontrivial steady-state solutions is proposed to predict waves propagation and waves run-up on coastal zones. The numerical m…
Numerical modelling of variable density shallow water flows with friction term
Amine Hanini, Abdelaziz Beljadid, Driss Ouazar
In this study, we focus on the modelling of coupled systems of shallow water flows and solute transport with source terms due to variable topography and friction effect. Our aim is…
Modelling of coupled surface and subsurface water flows
Hasan Karjoun, Abdelaziz Beljadid
In this paper, we propose to use the HLL finite volume scheme combined with implicit techniques for modelling the coupled surface and subsurface water flows. In our approach, we us…
Implicit and semi-implicit second-order time stepping methods for the Richards equation
Keita Sana, Beljadid Abdelaziz, Bourgault Yves
This study concerns numerical methods for efficiently solving the Richards equation where different weak formulations and computational techniques are analyzed. The spatial discret…
Modeling of unsaturated flow through porous media using meshless methods
Mohamed Boujoudar, Abdelaziz Beljadid, Ahmed Taik
In this study, we focus on the modelling of infiltration process in porous media. We use the meshless techniques for efficiently solving the Richards equation which describes unsat…
A well-balanced positivity preserving cell-vertex finite volume method satisfying the discrete maximum-minimum principle for coupled models of surface water flow and scalar transport
Hasan Karjoun, Abdelaziz Beljadid, Philippe G. LeFloch
We develop a new finite volume method using unstructured mesh-vertex grids for coupled systems modeling shallow water flows and solute transport over complex bottom topography. Nov…
Mass-conservative and positivity preserving second-order semi-implicit methods for high-order parabolic equations
Sana Keita, Abdelaziz Beljadid, Yves Bourgault
We consider a class of finite element approximations for fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary vari…
Efficient second-order semi-implicit finite element method for fourth-order nonlinear diffusion equations
Sana Keita, Abdelaziz Beljadid, Yves Bourgault
We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel secon…
A central-upwind geometry-preserving method for hyperbolic conservation laws on the sphere
Abdelaziz Beljadid, Philippe G. LeFloch
We introduce a second-order, central-upwind finite volume method for the discretization of nonlinear hyperbolic conservation laws posed on the two-dimensional sphere. The semi-disc…