Papers by Fayssal Benkhaldoun
Lecture Notes in Computer Science, 2023
Lecture Notes in Computer Science, 2023
Advances in Computational Mathematics, Jun 20, 2019
This paper deals with the numerical solution of an ionization wave propagation in air, described ... more This paper deals with the numerical solution of an ionization wave propagation in air, described by a coupled set of convection-diffusion-reaction equations and a Poisson equation. The standard three-species and more complex eleven-species models with simple chemistry are formulated. The PDEs are solved by a finite volume method that is theoretically second order in space and time on an unstructured adaptive grid. The upwind scheme and the diamond scheme are used for the discretization of the convective and diffusive fluxes, respectively. The Poisson equation is also discretized by the diamond scheme. The results of both models are compared in details for a test case. The influence of physically pertinent boundary conditions at electrodes is also presented. Finally, we deal with numerical accuracy study of implicit scheme in two variants for simplified standard model. It allows us in the future to compute simultaneously and efficiently a process consisting of short time discharge propagation and long-term after-discharge phase or repetitively pulsed discharge.
Journal of Elliptic and Parabolic Equations
Mathematical Methods in the Applied Sciences
We propose a class of finite volume algorithms that are both simple and efficient for solving num... more We propose a class of finite volume algorithms that are both simple and efficient for solving numerically the shallow water equations with varying densities; shallow water flows in single and two layers are considered. In these flow regimes, variable horizontal or vertical density is taken into account. The shallow water equations for the hydraulic variables are coupled with a suspended sediment transport equation for the concentration variable to construct the model. To approximate the numerical solution of the models under consideration, a generalized Rusanov method is proposed; this method avoids solving Riemann problems during the time integration process, and it is simple and accurate. The proposed method is divided into two stages: predictor and corrector; the presented finite volume approach is well balanced, conservative, and simple. Non‐oscillatory and suitable for shallow water equations when Riemann problems are challenging to solve. Several test problems for single‐layer...
Mathematical Methods in the Applied Sciences
Large-Scale Scientific Computing, 2022
Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, 2020
In this note, we establish a finite volume scheme for a model of a second order hyperbolic equati... more In this note, we establish a finite volume scheme for a model of a second order hyperbolic equation with a time delay in any space dimension. This model is considered in [10, 11] where some exponential stability estimates and oscillatory behaviour are proved. The scheme we shall present uses, as space discretization, the general class of nonconforming finite volume meshes of [5]. In addition to the proof of the existence and uniqueness of the discrete solution, we develop a new discrete a priori estimate. Thanks to this a priori estimate, we prove error estimates in discrete seminorms of \(L^\infty (H^1_0)\), \(L^\infty (L^2)\), and \(W^{1,\infty }(L^2)\). This work can be viewed as extension to the previous ones [2, 4] which dealt with the analysis of finite volume methods for respectively semilinear parabolic equations with a time delay and the wave equation.
Large-Scale Scientific Computing, 2020
SUSHI (Scheme Using Stabilization and Hybrid Interfaces) is a finite volume method has been devel... more SUSHI (Scheme Using Stabilization and Hybrid Interfaces) is a finite volume method has been developed at the first time to approximate heterogeneous and anisotropic diffusion problems. It has been applied later to approximate several types of partial differential equations. The main feature of SUSHI is that the control volumes can only be assumed to be polyhedral. Further, a consistent and stable Discrete Gradient is developed.
The European Physical Journal Plus, 2016
Abstract.In this work, we introduce a finite volume method for numerical simulation of shallow wa... more Abstract.In this work, we introduce a finite volume method for numerical simulation of shallow water equations with source terms in one and two space dimensions, and one-pressure model of two-phase flows in one space dimension. The proposed method is composed of two steps. The first, called predictor step, depends on a local parameter allowing to control the numerical diffusion. A strategy based on limiters theory enables to control this parameter. The second step recovers the conservation equation. The scheme can thus be turned to order 1 in the regions where the flow has a strong variation, and order 2 in the regions where the flow is regular. The numerical scheme is applied to several test cases in one and two space dimensions. This scheme demonstrates its well-balanced property, and that it is an efficient and accurate approach for solving shallow water equations with and without source terms, and water faucet problem.
Http Www Theses Fr, 2005
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Presented paper describes a numerical study of discharge plasma motion. This non-stationary pheno... more Presented paper describes a numerical study of discharge plasma motion. This non-stationary phenomenon with steep gradients and sharp peaks in unknowns is described as a coupled problem of convection-diffusion equation with source term for electron, ion densities and Poisson's equation for electric potential. The numerical method is 2nd order of accuracy in space and time and it uses dynamical adaptation of unstructured triangular mesh. Results of numerical studies included size of computational domain, type of boundary conditions and numerical convergence test are presented.
FVCA4, HPS, F. Benkhaldoun, D. Ouazar ( …, 2005
Flow, Turbulence and Combustion, 2006
In this work we consider a two steps finite volume scheme, recently developed to solve nonhomogen... more In this work we consider a two steps finite volume scheme, recently developed to solve nonhomogeneous systems. The first step of the scheme depends on a diffusion control parameter which we modulate, using the limiters theory. Results on Shallow water equations and two phase flows are presented. Keywords Non homogeneous systems . Finite volumes . SRNHR scheme F. Benkhaldoun ( ) • L.
Topical Problems of Fluid Mechanics 2017, 2017
Fluids
In this paper, a new rheological model for the flow of phosphate-water suspensions is proposed. T... more In this paper, a new rheological model for the flow of phosphate-water suspensions is proposed. The model’s ability to replicate the rheological characteristics of phosphate-water suspensions under different shear rate conditions is evaluated using rheometric tests, and it is found to be in good agreement with experimental data. A comprehensive methodology for obtaining the model parameters is presented. The proposed model is then incorporated into the OpenFoam numerical code. The results demonstrate that the model is capable of reproducing the rheological behavior of phosphate suspensions at both low and high concentrations by comparing it with suitable models for modeling the rheological behavior of phosphate suspensions. The proposed model can be applied to simulate and monitor phosphate slurry flows in industrial applications.
Algorithms
In this paper, an innovative methodology to handle the numerical simulation of viscoplastic flows... more In this paper, an innovative methodology to handle the numerical simulation of viscoplastic flows is proposed based on a multigrid initialization algorithm in conjunction with the SIMPLE procedure. The governing equations for incompressible flow, which consist of continuity and momentum equations, are solved on a collocated grid by combining the finite volume discretization and Rhie and chow interpolation for pressure–velocity coupling. Using the proposed solver in combination with the regularization scheme of Papanastasiou, we chose the square lid-driven cavity flow and pipe flow as test cases for validation and discussion. In doing so, we study the influence of the Bingham number and the Reynolds number on the development of rigid areas and the features of the vortices within the flow domain. Pipe flow results illustrate the flow’s response to the stress growth parameter values. We show that the representation of the yield surface and the plug zone is influenced by the chosen valu...
arXiv (Cornell University), May 24, 2021
The present paper describes a parallel unstructured-mesh Plasma simulation code based on Finite V... more The present paper describes a parallel unstructured-mesh Plasma simulation code based on Finite Volume method. The code dynamically refines and coarses mesh for accurate resolution of the different features regarding the electron density. Our purpose is to examine the performance of a new Parallel Adaptive Mesh Refinement (PAMR) procedure introduced on the ADAPT platform, which resolves of a relatively complicated system coupling the flow partial differential equations to the Poisson's equation. The implementation deals with the MUMPS parallel multi-frontal direct solver and mesh partitioning methods using METIS to improve the performance of the framework. The standard MPI is used to establish communication between processors. Performance analysis of the PAMR procedure shows the efficiency and the potential of the method for the propagation equations of ionization waves.
Springer Proceedings in Mathematics & Statistics, 2017
Adaptive unstructured finite volume methods for ionization waves are receiving increased attentio... more Adaptive unstructured finite volume methods for ionization waves 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. Our purpose is to examine the numerical performance of a new criteria for mesh adaptation which account only for the elliptic equation for the electric potential. The proposed adaptive finite volume method has important advantages in the discretization of the gradient fluxes and diffusion terms using unstructured grids and satisfies the conservation property. Numerical results are presented for a propagation of ionization waves in a rectangular domain.
Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, 2020
We present a finite volume model for the simulation of floods in urban areas. The model consists ... more 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 the significant reduction of the computational cost while preserving an acceptable level of accuracy. The finite volume method uses a modified Roe’s scheme involving the sign of the Jacobian matrix in the system for the discretization of gradient fluxes. The performance of the numerical model is demonstrated by comparing the results obtained using the proposed method to laboratory experiments for a flow problem over an array of obstacles.
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Papers by Fayssal Benkhaldoun