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Dr Mohammed Seaid's Outputs (147)

High-order spline finite element method for solving time-dependent electromagnetic waves (2024)
Journal Article
El-Barkani, I., El-Hadouti, I., Addam, M., & Seaid, M. (2024). High-order spline finite element method for solving time-dependent electromagnetic waves. Applied Numerical Mathematics, 206, 48-74. https://doi.org/10.1016/j.apnum.2024.08.002

In this paper we propose a high-order spline finite element method for solving a class of time-dependent electromagnetic waves and its associated frequency-domain approach. A Fourier transform and its inverse are used for the time integration of the... Read More about High-order spline finite element method for solving time-dependent electromagnetic waves.

Future projection of droughts in Morocco and potential impact on agriculture (2024)
Journal Article
Gumus, V., El Moçayd, N., Seker, M., & Seaid, M. (2024). Future projection of droughts in Morocco and potential impact on agriculture. Journal of Environmental Management, 367, Article 122019. https://doi.org/10.1016/j.jenvman.2024.122019


The present study evaluates the future drought hazard in Morocco using a Multi-Model Ensemble (MME) approach. First, the artificial neural network-based MME is constructed using the General Circulation Models (GCMs) from the Climat... Read More about Future projection of droughts in Morocco and potential impact on agriculture.

Unsupervised stochastic learning and reduced order modelling for global sensitivity analysis in cardiac electrophysiology models (2024)
Journal Article
El Moçayd, N., Belhamadia, Y., & Seaid, M. (in press). Unsupervised stochastic learning and reduced order modelling for global sensitivity analysis in cardiac electrophysiology models. Computer Methods and Programs in Biomedicine, https://doi.org/10.1016/j.cmpb.2024.108311


Background and Objective:
Numerical simulations in electrocardiology are often affected by various uncertainties inherited from the lack of precise knowledge regarding input values including those related to the c... Read More about Unsupervised stochastic learning and reduced order modelling for global sensitivity analysis in cardiac electrophysiology models.

Climate-informed flood risk mapping using a GAN-based approach (ExGAN) (2024)
Journal Article
Belhajjam, R., Chaqdid, A., Yebari, N., Seaid, M., & Moçayd, N. E. (2024). Climate-informed flood risk mapping using a GAN-based approach (ExGAN). Journal of Hydrology, 638, Article 131487. https://doi.org/10.1016/j.jhydrol.2024.131487

This study develops a class of robust models for flood risk mapping in highly vulnerable regions by focusing on accurately depicting extreme precipitation patterns aligned with regional climates. By implementing sophisticated hydrodynamics modeling a... Read More about Climate-informed flood risk mapping using a GAN-based approach (ExGAN).

A time viscosity-splitting method for incompressible flows with temperature-dependent viscosity and thermal conductivity (2024)
Journal Article
El-Amrani, M., Obbadi, A., Seaid, M., & Yakoubi, D. (2024). A time viscosity-splitting method for incompressible flows with temperature-dependent viscosity and thermal conductivity. Computer Methods in Applied Mechanics and Engineering, 429, Article 117103. https://doi.org/10.1016/j.cma.2024.117103

A fractional-step method is proposed and analyzed for solving the incompressible thermal Navier–Stokes equations coupled to the convection–conduction equation for heat transfer with a generalized source term for which the viscosity and thermal conduc... Read More about A time viscosity-splitting method for incompressible flows with temperature-dependent viscosity and thermal conductivity.

An improved splitting algorithm for unsteady generalized Newtonian fluid flow problems with natural boundary conditions (2024)
Journal Article
Obbadi, A., El-Amrani, M., Seaid, M., & Yakoubi, D. (2024). An improved splitting algorithm for unsteady generalized Newtonian fluid flow problems with natural boundary conditions. Computers and Mathematics with Applications, 167, 92-109. https://doi.org/10.1016/j.camwa.2024.05.010

Generalized Newtonian fluids are challenging to solve using the standard projection or fractional-step methods which split the diffusion term from the incompressibility constraint during the time integration process. Most of this class numerical meth... Read More about An improved splitting algorithm for unsteady generalized Newtonian fluid flow problems with natural boundary conditions.

Modelling and simulation of pollution transport in the Mediterranean Sea using enriched finite element method (2024)
Journal Article
El-Amrani, M., Ouardghi, A., & Seaid, M. (2024). Modelling and simulation of pollution transport in the Mediterranean Sea using enriched finite element method. Mathematics and Computers in Simulation, 223, 565-587. https://doi.org/10.1016/j.matcom.2024.04.028

This paper presents a novel numerical method for simulating the transport and dispersion of pollutants in the Mediterranean sea. The governing mathematical equations consist of a barotropic ocean model with friction terms, bathymetric forces, Corioli... Read More about Modelling and simulation of pollution transport in the Mediterranean Sea using enriched finite element method.

UKACM Proceedings 2024 (2024)
Presentation / Conference Contribution
(2024, April). UKACM Proceedings 2024. Presented at 2024 UK Association for Computational Mechanics Conference, Durham, UK

The proceedings present 52 scientific papers written for the 32nd conference of the UK Association for Computational Mechanics (UKACM). The papers submitted to UKACM 2024 cover the breadth of computational mechanics research within the UK and beyond... Read More about UKACM Proceedings 2024.

Directional enrichment functions for finite element solutions of transient anisotropic diffusion (2024)
Journal Article
Bahssini, A., Izem, N., Mohamed, M. S., & Seaid, M. (in press). Directional enrichment functions for finite element solutions of transient anisotropic diffusion. Computers and Mathematics with Applications, 163, 42-55. https://doi.org/10.1016/j.camwa.2024.03.016


The present study proposes a novel approach for efficiently solving an anisotropic transient diffusion problem using an enriched finite element method. We develop directional enrichment for the finite elements in the spatial discre... Read More about Directional enrichment functions for finite element solutions of transient anisotropic diffusion.

A fully coupled dynamic water-mooring line system: Numerical implementation and applications (2024)
Journal Article
Zheng, X., Seaid, M., & Osman, A. S. (2024). A fully coupled dynamic water-mooring line system: Numerical implementation and applications. Ocean Engineering, 294, Article 116792. https://doi.org/10.1016/j.oceaneng.2024.116792

Several numerical challenges exist in the analysis of water-mooring line systems which require robust, yet practical, methods to address this type of fully coupled nonlinear dynamic problems. The present study proposes a novel class of numerical tech... Read More about A fully coupled dynamic water-mooring line system: Numerical implementation and applications.

Error estimates for a viscosity-splitting scheme in time applied to non-Newtonian fluid flows (2023)
Journal Article
El-Amrani, M., Obbadi, A., Seaid, M., & Yakoubi, D. (2024). Error estimates for a viscosity-splitting scheme in time applied to non-Newtonian fluid flows. Computer Methods in Applied Mechanics and Engineering, 419, Article 116639. https://doi.org/10.1016/j.cma.2023.116639

A time fractional-step method is presented for numerical solutions of the incompressible non-Newtonian fluids for which the viscosity is non-linear depending on the shear-rate magnitude according to a generic model. The method belongs to a class of v... Read More about Error estimates for a viscosity-splitting scheme in time applied to non-Newtonian fluid flows.

A fast and accurate method for transport and dispersion of phosphogypsum in coastal zones: Application to Jorf Lasfar (2023)
Journal Article
Ouardghi, A., Seaid, M., El‐Amrani, M., & El Mocayd, N. (2023). A fast and accurate method for transport and dispersion of phosphogypsum in coastal zones: Application to Jorf Lasfar. International Journal for Numerical Methods in Fluids, 96(3), 336-363. https://doi.org/10.1002/fld.5248

We present a numerical method for modelling and simulation of transport and dispersion of phosphogypsum in the Jorf Lasfar coastal zone located on the Atlantic Ocean at Morocco. The governing equations consist of the well-established barotropic ocean... Read More about A fast and accurate method for transport and dispersion of phosphogypsum in coastal zones: Application to Jorf Lasfar.

Convergence analysis of a class of iterative methods for propagation of reaction fronts in porous media (2023)
Journal Article
Salhi, L., Seaid, M., & Yakoubi, D. (2024). Convergence analysis of a class of iterative methods for propagation of reaction fronts in porous media. Computer Methods in Applied Mechanics and Engineering, 418(Part A), Article 116524. https://doi.org/10.1016/j.cma.2023.116524

We present an iterative scheme for the numerical analysis of propagating reaction front problems in porous media satisfying an Arrhenius-type law. The governing equations consist of the Darcy equations for the pressure and flow field coupled to two c... Read More about Convergence analysis of a class of iterative methods for propagation of reaction fronts in porous media.

A material point/finite volume method for coupled shallow water flows and large dynamic deformations in seabeds (2023)
Journal Article
Zheng, X., Seaid, M., Pisanò, F., Hicks, M. A., Vardon, P. J., Huvaj, N., & Osman, A. S. (2023). A material point/finite volume method for coupled shallow water flows and large dynamic deformations in seabeds. Computers and Geotechnics, 162(October), Article 105673. https://doi.org/10.1016/j.compgeo.2023.105673

A hybrid material point/finite volume method for the numerical simulation of shallow water waves caused by large dynamic deformations in the bathymetry is presented. The proposed model consists of coupling the nonlinear shallow water equations for th... Read More about A material point/finite volume method for coupled shallow water flows and large dynamic deformations in seabeds.

Evaluation of future temperature and precipitation projections in Morocco using the ANN-based multi-model ensemble from CMIP6 (2023)
Journal Article
Gumus, V., El Moçayd, N., Seker, M., & Seaid, M. (2023). Evaluation of future temperature and precipitation projections in Morocco using the ANN-based multi-model ensemble from CMIP6. Atmospheric Research, 292, Article 106880. https://doi.org/10.1016/j.atmosres.2023.106880

In present study, values of minimum temperature, maximum temperature and precipitation at 27 observation stations in Morocco are used to implement an artificial neural network based downscaling approach in order to simulate regional climate and to in... Read More about Evaluation of future temperature and precipitation projections in Morocco using the ANN-based multi-model ensemble from CMIP6.

Computing enhancement of the nonlinear SPN approximations of radiative heat transfer in participating material (2023)
Journal Article
Belhamadia, Y., & Seaid, M. (2023). Computing enhancement of the nonlinear SPN approximations of radiative heat transfer in participating material. Journal of Computational and Applied Mathematics, 434, Article 115342. https://doi.org/10.1016/j.cam.2023.115342

Anisotropic mesh adaptation is an efficient procedure for controlling the output error of finite element simulations, particularly when used for three-dimensional problems. In this paper, we present an enhanced computational algorithm based on an ani... Read More about Computing enhancement of the nonlinear SPN approximations of radiative heat transfer in participating material.

Novel adaptive finite volume method on unstructured meshes for time-domain wave scattering and diffraction (2023)
Journal Article
Ghoudi, T., Mohamed, M. S., & Seaid, M. (2023). Novel adaptive finite volume method on unstructured meshes for time-domain wave scattering and diffraction. Computers and Mathematics with Applications, 141, https://doi.org/10.1016/j.camwa.2023.03.025

A new adaptive finite volume method is proposed for the simulation of the wave problems in the time domain. The transient wave equations are discretized in time and space. A vertex-centered finite volume method is constructed with both cell-centered... Read More about Novel adaptive finite volume method on unstructured meshes for time-domain wave scattering and diffraction.

A Bernstein–Bézier Lagrange–Galerkin method for three-dimensional advection-dominated problems (2022)
Journal Article
El-Amrani, M., Kacimi, A. E., Khouya, B., & Seaid, M. (2023). A Bernstein–Bézier Lagrange–Galerkin method for three-dimensional advection-dominated problems. Computer Methods in Applied Mechanics and Engineering, 403, Article 115758. https://doi.org/10.1016/j.cma.2022.115758

We present a high-order Bernstein–Bézier finite element discretization to accurately solve three-dimensional advection-dominated problems on unstructured tetrahedral meshes. The key idea consists of implementing a modified method of characteristics t... Read More about A Bernstein–Bézier Lagrange–Galerkin method for three-dimensional advection-dominated problems.

An iterative scheme for solving a coupled Darcy–convection–diffusion model (2022)
Journal Article
El-Amrani, M., Salhi, L., Seaid, M., & Yakoubi, D. (2023). An iterative scheme for solving a coupled Darcy–convection–diffusion model. Journal of Mathematical Analysis and Applications, 517(2), Article 126603. https://doi.org/10.1016/j.jmaa.2022.126603

We present an iterative scheme for the numerical analysis of a class of coupled Darcy-convection-diffusion problems modelling flow and heat transfer in porous media. The governing equations consist of the Darcy equations for the flow coupled to a con... Read More about An iterative scheme for solving a coupled Darcy–convection–diffusion model.

Bernstein-Bézier Galerkin-Characteristics Finite Element Method for Convection-Diffusion Problems (2022)
Journal Article
El-Amrani, M., El-Kacimi, A., Khouya, B., & Seaid, M. (2022). Bernstein-Bézier Galerkin-Characteristics Finite Element Method for Convection-Diffusion Problems. Journal of Scientific Computing, 92(2), Article 58. https://doi.org/10.1007/s10915-022-01888-7

A class of Bernstein-Bézier basis based high-order finite element methods is developed for the Galerkin-characteristics solution of convection-diffusion problems. The Galerkin-characteristics formulation is derived using a semi-Lagrangian discretizat... Read More about Bernstein-Bézier Galerkin-Characteristics Finite Element Method for Convection-Diffusion Problems.

Simplified finite element approximations for coupled natural convection and radiation heat transfer (2022)
Journal Article
Albadr, J., El-Amrani, M., & Seaid, M. (2023). Simplified finite element approximations for coupled natural convection and radiation heat transfer. Numerical Heat Transfer, Part A Applications, 83(5), 478-502. https://doi.org/10.1080/10407782.2022.2091897

This article focuses on the effect of radiative heat on natural convection heat transfer in a square domain inclined with an angle. The left vertical wall of the enclosure is heated while maintaining the vertical right wall at room temperature with b... Read More about Simplified finite element approximations for coupled natural convection and radiation heat transfer.

A Well-Balanced Runge-Kutta Discontinuous Galerkin Method for Multilayer Shallow Water Equations with Non-Flat Bottom Topography (2022)
Journal Article
Izem, N., & Seaid, M. (2022). A Well-Balanced Runge-Kutta Discontinuous Galerkin Method for Multilayer Shallow Water Equations with Non-Flat Bottom Topography. Advances in applied mathematics and mechanics, 14(3), 725-758. https://doi.org/10.4208/aamm.oa-2020-0364

A well-balanced Runge-Kutta discontinuous Galerkin method is presented for the numerical solution of multilayer shallow water equations with mass exchange and non-flat bottom topography. The governing equations are reformulated as a nonlinear system... Read More about A Well-Balanced Runge-Kutta Discontinuous Galerkin Method for Multilayer Shallow Water Equations with Non-Flat Bottom Topography.

A Cell-Centered Semi-Lagrangian Finite Volume Method for Solving Two-Dimensional Coupled Burgers’ Equations (2022)
Journal Article
Asmouh, I., El-Amrani, M., Seaid, M., & Yebari, N. (2022). A Cell-Centered Semi-Lagrangian Finite Volume Method for Solving Two-Dimensional Coupled Burgers’ Equations. Computational and mathematical methods, 2022, Article 8192192. https://doi.org/10.1155/2022/8192192

A cell-centered finite volume semi-Lagrangian method is presented for the numerical solution of two-dimensional coupled Burgers’ problems on unstructured triangular meshes. The method combines a modified method of characteristics for the time integra... Read More about A Cell-Centered Semi-Lagrangian Finite Volume Method for Solving Two-Dimensional Coupled Burgers’ Equations.

A surrogate model for efficient quantification of uncertainties in multilayer shallow water flows (2021)
Journal Article
Al-Ghosoun, A., El Moçayd, N., & Seaid, M. (2021). A surrogate model for efficient quantification of uncertainties in multilayer shallow water flows. Environmental Modelling and Software, 144, Article 105176. https://doi.org/10.1016/j.envsoft.2021.105176

In this study, we investigate the implementation of a Proper Orthogonal Decomposition (POD) Polynomial Chaos Expansion (PCE) POD-PCE surrogate model for the propagation and quantification of the uncertainty in hydraulic modelling. The considered mode... Read More about A surrogate model for efficient quantification of uncertainties in multilayer shallow water flows.

Data-driven polynomial chaos expansions for characterization of complex fluid rheology: Case study of phosphate slurry (2021)
Journal Article
El Moçayd, N., & Seaid, M. (2021). Data-driven polynomial chaos expansions for characterization of complex fluid rheology: Case study of phosphate slurry. Reliability Engineering & System Safety, 216, https://doi.org/10.1016/j.ress.2021.107923

Mine transportation through hydraulic pipelines is increasingly used by various industries around the world. In Morocco, this has been implemented for the case of phosphate transportation. This allows to increase the production and reduce the transpo... Read More about Data-driven polynomial chaos expansions for characterization of complex fluid rheology: Case study of phosphate slurry.

A boundary element method formulation based on the Caputo derivative for the solution of the diffusion-wave equation (2021)
Journal Article
Carrer, J., Solheid, B., Trevelyan, J., & Seaid, M. (online). A boundary element method formulation based on the Caputo derivative for the solution of the diffusion-wave equation. Engineering with Computers, https://doi.org/10.1007/s00366-021-01480-x

A boundary element method formulation is developed and validated through the solution of problems governed by the diffusion-wave equation, for which the order of the time derivative, say α, ranges in the interval (1, 2). This fractional time derivati... Read More about A boundary element method formulation based on the Caputo derivative for the solution of the diffusion-wave equation.

An enriched Galerkin-characteristics finite element method for convection-dominated and transport problems (2021)
Journal Article
Ouardghi, A., El-Amrani, M., & Seaid, M. (2021). An enriched Galerkin-characteristics finite element method for convection-dominated and transport problems. Applied Numerical Mathematics, 167, 119-142. https://doi.org/10.1016/j.apnum.2021.04.018

We propose an enriched Galerkin-characteristics finite element method for numerical solution of convection-dominated problems. The method uses the modified method of characteristics for the integration of the total derivative in time, combined with t... Read More about An enriched Galerkin-characteristics finite element method for convection-dominated and transport problems.

Non-intrusive polynomial chaos methods for uncertainty quantification in wave problems at high frequencies (2021)
Journal Article
Mocayd, N. E., Mohamed, M. S., & Seaid, M. (2021). Non-intrusive polynomial chaos methods for uncertainty quantification in wave problems at high frequencies. Journal of Computational Science, 53, Article 101344. https://doi.org/10.1016/j.jocs.2021.101344

Numerical solutions of wave problems are often influenced by uncertainties generated by a lack of knowledge of the input values related to the domain data and/or boundary conditions in the mathematical equations used in the modeling. Conventional met... Read More about Non-intrusive polynomial chaos methods for uncertainty quantification in wave problems at high frequencies.

A Computational Model for Simulation of Shallow Water Waves by Elastic Deformations in the Topography (2021)
Journal Article
Al-Ghosoun, A., Osman, A., & Seaid, M. (online). A Computational Model for Simulation of Shallow Water Waves by Elastic Deformations in the Topography. Communications in computational physics, https://doi.org/10.4208/cicp.oa-2020-0098

We propose a coupled model to simulate shallow water waves induced by elastic deformations in the bed topography. The governing equations consist of the depth-averaged shallow water equations including friction terms for the water freesurface and the... Read More about A Computational Model for Simulation of Shallow Water Waves by Elastic Deformations in the Topography.

A hybrid finite volume/finite element method for shallow water waves by static deformation on seabeds (2020)
Journal Article
Al-Ghosoun, A., Osman, A., & Seaid, M. (2021). A hybrid finite volume/finite element method for shallow water waves by static deformation on seabeds. Engineering Computations, 38(5), 2434-2459. https://doi.org/10.1108/ec-05-2020-0275

Purpose The purpose of this study is twofold: first, to derive a consistent model free-surface runup flow problems over deformable beds. The authors couple the nonlinear one-dimensional shallow water equations, including friction terms for the water... Read More about A hybrid finite volume/finite element method for shallow water waves by static deformation on seabeds.

Fast inverse solver for identifying the diffusion coefficient in time-dependent problems using noisy data (2020)
Journal Article
Jiang, J., Shadi Mohamed, M., Seaid, M., & Li, H. (2021). Fast inverse solver for identifying the diffusion coefficient in time-dependent problems using noisy data. Archive of Applied Mechanics, 91(4), 1623-1639. https://doi.org/10.1007/s00419-020-01844-7

We propose an efficient inverse solver for identifying the diffusion coefficient based on few random measurements which can be contaminated with noise. We focus mainly on problems involving solutions with steep heat gradients common with sudden chang... Read More about Fast inverse solver for identifying the diffusion coefficient in time-dependent problems using noisy data.

A boundary element method formulation based on the Caputo derivative for the solution of the anomalous diffusion problem (2020)
Journal Article
Carrer, J., Solheid, B., Trevelyan, J., & Seaid, M. (2021). A boundary element method formulation based on the Caputo derivative for the solution of the anomalous diffusion problem. Engineering Analysis with Boundary Elements, 122, 132-144. https://doi.org/10.1016/j.enganabound.2020.10.017

This work presents a boundary element method formulation for the solution of the anomalous diffusion problem. By keeping the fractional time derivative as it appears in the governing differential equation of the problem, and by employing a Weighted R... Read More about A boundary element method formulation based on the Caputo derivative for the solution of the anomalous diffusion problem.

A Conservative Semi-Lagrangian Finite Volume Method for Convection–Diffusion Problems on Unstructured Grids (2020)
Journal Article
Asmouh, I., El-Amrani, M., Seaid, M., & Yebari, N. (2020). A Conservative Semi-Lagrangian Finite Volume Method for Convection–Diffusion Problems on Unstructured Grids. Journal of Scientific Computing, 85(1), Article 11. https://doi.org/10.1007/s10915-020-01316-8

A conservative semi-Lagrangian finite volume method is presented for the numerical solution of convection–diffusion problems on unstructured grids. The new method consists of combining the modified method of characteristics with a cell-centered finit... Read More about A Conservative Semi-Lagrangian Finite Volume Method for Convection–Diffusion Problems on Unstructured Grids.

Numerical solution of Rosseland model for transient thermal radiation in non-grey optically thick media using enriched basis functions (2020)
Journal Article
Malek, M., Izem, N., Mohamed, M. S., Seaid, M., & Wakrim, M. (2021). Numerical solution of Rosseland model for transient thermal radiation in non-grey optically thick media using enriched basis functions. Mathematics and Computers in Simulation, 180, 258-275. https://doi.org/10.1016/j.matcom.2020.08.024

Heat radiation in optically thick non-grey media can be well approximated with the Rosseland model which is a class of nonlinear diffusion equations with convective boundary conditions. The optical spectrum is divided into a set of finite bands with... Read More about Numerical solution of Rosseland model for transient thermal radiation in non-grey optically thick media using enriched basis functions.

Two-dimensional numerical modelling of shallow water flows over multilayer movable beds (2020)
Journal Article
Rowan, T., & Seaid, M. (2020). Two-dimensional numerical modelling of shallow water flows over multilayer movable beds. Applied Mathematical Modelling, 88, Article 474-497. https://doi.org/10.1016/j.apm.2020.06.052

The two-dimensional modelling of shallow water flows over multi-sediment erodible beds is presented. A novel approach is developed for the treatment of multiple sediment types in morphodynamics. The governing equations include the two-dimensional sha... Read More about Two-dimensional numerical modelling of shallow water flows over multilayer movable beds.

A Three-Dimensional Monotonicity-Preserving Modified Method of Characteristics on Unstructured Tetrahedral Meshes (2020)
Journal Article
Khouya, B., El-Amrani, M., & Seaid, M. (2020). A Three-Dimensional Monotonicity-Preserving Modified Method of Characteristics on Unstructured Tetrahedral Meshes. International Journal of Computational Methods, 18(01), https://doi.org/10.1142/s0219876220500279

Slope limiters have been widely used to eliminate nonphysical oscillations near discontinuities generated by finite volume methods for hyperbolic systems of conservation laws. In this study, we investigate the performance of these limiters as applied... Read More about A Three-Dimensional Monotonicity-Preserving Modified Method of Characteristics on Unstructured Tetrahedral Meshes.

Partition of Unity Finite Element Analysis of Nonlinear Transient Diffusion Problems Using p-Version Refinement (2020)
Journal Article
El Kahoui, A., Malek, M., Izem, N., Shadi Mohamed, M., & Seaid, M. (2020). Partition of Unity Finite Element Analysis of Nonlinear Transient Diffusion Problems Using p-Version Refinement. Computer Modeling in Engineering & Sciences, 124(1), 61-78. https://doi.org/10.32604/cmes.2020.010874

We propose a high-order enriched partition of unity finite element method for linear and nonlinear time-dependent diffusion problems. The solution of this class of problems often exhibits non-smooth features such as steep gradients and boundary layer... Read More about Partition of Unity Finite Element Analysis of Nonlinear Transient Diffusion Problems Using p-Version Refinement.

The Boundary Element Method applied to the solution of the Diffusion-Wave problem (2020)
Journal Article
Carrer, J., Solheid, B., Trevelyan, J., & Seaid, M. (2020). The Boundary Element Method applied to the solution of the Diffusion-Wave problem. Engineering Analysis with Boundary Elements, 117, 13-25. https://doi.org/10.1016/j.enganabound.2020.03.027

A Boundary Element Method formulation is developed for the solution of the two-dimensional diffusion-wave problem, which is governed by a partial differential equation presenting a time fractional derivative of order α, with 1.0 < α < 2.0. In the pro... Read More about The Boundary Element Method applied to the solution of the Diffusion-Wave problem.

A three-dimensional enriched finite element method for nonlinear transient heat transfer in functionally graded materials (2020)
Journal Article
Malek, M., Izem, N., Mohamed M, S., & Seaid, M. (2020). A three-dimensional enriched finite element method for nonlinear transient heat transfer in functionally graded materials. International Journal of Heat and Mass Transfer, 155, Article 119804. https://doi.org/10.1016/j.ijheatmasstransfer.2020.119804

Nonlinear transient heat transfer in functionally graded materials is being studied more popular in present. In preliminary design, this problem can be simplified as a composite, and a three-dimensional transient heat transfer analysis is used to adj... Read More about A three-dimensional enriched finite element method for nonlinear transient heat transfer in functionally graded materials.

Stochastic model reduction for polynomial chaos expansion of acoustic waves using proper orthogonal decomposition (2019)
Journal Article
El Moçayd, N., Shadi Mohamed, M., Ouazar, D., & Seaid, M. (2020). Stochastic model reduction for polynomial chaos expansion of acoustic waves using proper orthogonal decomposition. Reliability Engineering & System Safety, 195, https://doi.org/10.1016/j.ress.2019.106733

We propose a non-intrusive stochastic model reduction method for polynomial chaos representation of acoustic problems using proper orthogonal decomposition. The random wavenumber in the well-established Helmholtz equation is approximated via the poly... Read More about Stochastic model reduction for polynomial chaos expansion of acoustic waves using proper orthogonal decomposition.

Multi-hp adaptive discontinuous Galerkin methods for simplified PN approximations of 3D radiative transfer in non-gray media (2019)
Journal Article
Giani, S., & Seaid, M. (2020). Multi-hp adaptive discontinuous Galerkin methods for simplified PN approximations of 3D radiative transfer in non-gray media. Applied Numerical Mathematics, 150, 252-273. https://doi.org/10.1016/j.apnum.2019.09.018

In this paper we present a multi-hp adaptive discontinuous Galerkin method for 3D simplified approximations of radiative transfer in non-gray media capable of reaching accuracies superior to most of methods in the literature. The simplified models ar... Read More about Multi-hp adaptive discontinuous Galerkin methods for simplified PN approximations of 3D radiative transfer in non-gray media.

The Boundary Element Method Applied to the Solution of the Anomalous Diffusion Problem (2019)
Journal Article
Carrer, J., Seaid, M., Trevelyan, J., & Solheid, B. (2019). The Boundary Element Method Applied to the Solution of the Anomalous Diffusion Problem. Engineering Analysis with Boundary Elements, 109, 129-142. https://doi.org/10.1016/j.enganabound.2019.09.016

A Boundary Element Method formulation is developed for the solution of the two-dimensional anomalous diffusion equation. Initially, the Riemann–Liouville Fractional derivative is applied on both sides of the partial differential equation (PDE), thus... Read More about The Boundary Element Method Applied to the Solution of the Anomalous Diffusion Problem.

Efficient computational models for shallow water flows over multilayer erodible beds (2019)
Journal Article
Rowan, T., & Seaid, M. (2019). Efficient computational models for shallow water flows over multilayer erodible beds. Engineering Computations, 37(2), 401-429. https://doi.org/10.1108/ec-10-2018-0470

Purpose: The purpose of this paper is to present a new numerical model for shallow water flows over heterogeneous sedimentary layers. It is already several years since the single-layered models have been used to model shallow water flows over erodibl... Read More about Efficient computational models for shallow water flows over multilayer erodible beds.

Explicit time integration with lumped mass matrix for enriched finite elements solution of time domain wave problems (2019)
Journal Article
Drolia, M., Mohamed, M., Laghrouche, O., Seaid, M., & El Kacimi, A. (2020). Explicit time integration with lumped mass matrix for enriched finite elements solution of time domain wave problems. Applied Mathematical Modelling, 77(2), 1273-1293. https://doi.org/10.1016/j.apm.2019.07.054

We present a partition of unity finite element method for wave propagation problems in the time domain using an explicit time integration scheme. Plane wave enrichment functions are introduced at the finite elements nodes which allows for a coarse me... Read More about Explicit time integration with lumped mass matrix for enriched finite elements solution of time domain wave problems.

Enhanced Conformal Perfectly Matched Layers for Bernstein-Bezier Finite Element Modelling of Short Wave Scattering (2019)
Journal Article
El-Kacimi, A., Laghrouche, O., Ouazar, D., Mohamed, M., Seaid, M., & Trevelyan, J. (2019). Enhanced Conformal Perfectly Matched Layers for Bernstein-Bezier Finite Element Modelling of Short Wave Scattering. Computer Methods in Applied Mechanics and Engineering, 355, 614-638. https://doi.org/10.1016/j.cma.2019.06.032

The aim of this paper is to accurately solve short wave scattering problems governed by the Helmholtz equation using the Bernstein-Bezier Finite Element method (BBFEM), combined with a conformal perfectly matched layer (PML). Enhanced PMLs, where cur... Read More about Enhanced Conformal Perfectly Matched Layers for Bernstein-Bezier Finite Element Modelling of Short Wave Scattering.

Identifying the wavenumber for the inverse Helmholtz problem using an enriched finite element formulation (2018)
Journal Article
Jiang, J., Mohamed, M. S., Seaid, M., & Li, H. (2018). Identifying the wavenumber for the inverse Helmholtz problem using an enriched finite element formulation. Computer Methods in Applied Mechanics and Engineering, 340, 615-629. https://doi.org/10.1016/j.cma.2018.06.014

We investigate the inverse problem of identifying the wavenumber for the Helmholtz equation. The problem solution is based on measurements taken at few points from inside the computational domain or on its boundary. A novel iterative approach is prop... Read More about Identifying the wavenumber for the inverse Helmholtz problem using an enriched finite element formulation.

Iterative solvers for generalized finite element solution of boundary-value problems (2018)
Journal Article
Mohamed, M. S., Seaid, M., & Bouhamidi, A. (2018). Iterative solvers for generalized finite element solution of boundary-value problems. Numerical Linear Algebra with Applications, 25(6), https://doi.org/10.1002/nla.2205

Most of generalized finite element methods use dense direct solvers for the resulting linear systems. This is mainly the case due to the ill‐conditioned linear systems that are associated with these methods. In this study, we investigate the performa... Read More about Iterative solvers for generalized finite element solution of boundary-value problems.

A new numerical treatment of moving wet/dry fronts in dam-break flows (2018)
Journal Article
Al-Ghosoun, A., Herty, M., & Seaid, M. (2018). A new numerical treatment of moving wet/dry fronts in dam-break flows. Journal of Applied Mathematics and Computing, 59(1-2), 489-516. https://doi.org/10.1007/s12190-018-1189-5

The aim of this paper is to present a new finite volume method for moving wet/dry fronts in shallow water flows. The method consists on reformulating the shallow water equations in a moving wetted domain where the wet/dry interface is located using t... Read More about A new numerical treatment of moving wet/dry fronts in dam-break flows.

Enriched finite elements for initial-value problem of transverse electromagnetic waves in time domain (2017)
Journal Article
Drolia, M., Mohamed, M., Laghrouche, O., Seaid, M., & Trevelyan, J. (2017). Enriched finite elements for initial-value problem of transverse electromagnetic waves in time domain. Computers and Structures, 182, 354-367. https://doi.org/10.1016/j.compstruc.2016.11.011

This paper proposes a partition of unity enrichment scheme for the solution of the electromagnetic wave equation in the time domain. A discretization scheme in time is implemented to render implicit solutions of systems of equations possible. The sch... Read More about Enriched finite elements for initial-value problem of transverse electromagnetic waves in time domain.

hp-adaptive discontinuous Galerkin methods for simplified PN approximations of frequency-dependent radiative transfer (2015)
Journal Article
Giani, S., & Seaid, M. (2016). hp-adaptive discontinuous Galerkin methods for simplified PN approximations of frequency-dependent radiative transfer. Computer Methods in Applied Mechanics and Engineering, 301, 52-79. https://doi.org/10.1016/j.cma.2015.12.013

We investigate the performance of a class of hp-adaptive discontinuous Galerkin methods for the numerical solution of simplified PN approximations of radiative transfer in non-grey semitransparent media. By introducing an optical scale and using asym... Read More about hp-adaptive discontinuous Galerkin methods for simplified PN approximations of frequency-dependent radiative transfer.

Projection finite volume method for shallow water flows (2015)
Journal Article
Benkhaldoun, F., Sari, S., & Seaid, M. (2015). Projection finite volume method for shallow water flows. Mathematics and Computers in Simulation, 118, 87-101. https://doi.org/10.1016/j.matcom.2014.11.027

A simple and accurate projection finite volume method is developed for solving shallow water equations in two space dimensions. The proposed approach belongs to the class of fractional-step procedures where the numerical fluxes are reconstructed usin... Read More about Projection finite volume method for shallow water flows.

A family of finite volume Eulerian–Lagrangian methods for two-dimensional conservation laws (2015)
Journal Article
Benkhaldoun, F., Sari, S., & Seaid, M. (2015). A family of finite volume Eulerian–Lagrangian methods for two-dimensional conservation laws. Journal of Computational and Applied Mathematics, 285, 181-202. https://doi.org/10.1016/j.cam.2015.02.014

We develop a family of finite volume Eulerian–Lagrangian methods for the solution of nonlinear conservation laws in two space dimensions. The proposed approach belongs to the class of fractional-step procedures where the numerical fluxes are reconstr... Read More about A family of finite volume Eulerian–Lagrangian methods for two-dimensional conservation laws.

A non-homogeneous Riemann solver for shallow water equations in porous media (2015)
Journal Article
Benkhaldoun, F., Elmahi, I., Moumna, A., & Seaid, M. (2016). A non-homogeneous Riemann solver for shallow water equations in porous media. Applicable Analysis, 95(10), 2181-2202. https://doi.org/10.1080/00036811.2015.1067304

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 poros... Read More about A non-homogeneous Riemann solver for shallow water equations in porous media.

Mixed enrichment for the finite element method in heterogeneous media (2014)
Journal Article
Diwan, G., Mohamed, M., Seaid, M., Trevelyan, J., & Laghrouche, O. (2015). Mixed enrichment for the finite element method in heterogeneous media. International Journal for Numerical Methods in Engineering, 101(1), 54-78. https://doi.org/10.1002/nme.4795

Problems of multiple scales of interest or of locally nonsmooth solutions may often involve heterogeneous media. These problems are usually very demanding in terms of computations with the conventional finite element method. On the other hand, differ... Read More about Mixed enrichment for the finite element method in heterogeneous media.

A Frequency-domain Approach for the P1 Approximation of Time-dependent Radiative Transfer (2014)
Journal Article
Addam, M., Bouhamidi, A., & Seaid, M. (2015). A Frequency-domain Approach for the P1 Approximation of Time-dependent Radiative Transfer. Journal of Scientific Computing, 62(3), 623-651. https://doi.org/10.1007/s10915-014-9870-9

We propose a new frequency-domain method to solve the simplified P1 approximation of time-dependent radiative transfer equations. The method employs the Fourier transform and consists of two stages. In the first stage the equations are transformed in... Read More about A Frequency-domain Approach for the P1 Approximation of Time-dependent Radiative Transfer.

A simple multi-layer finite volume solver for density-driven shallow water flows (2014)
Journal Article
Benkhaldoun, F., Sari, S., & Seaid, M. (2014). A simple multi-layer finite volume solver for density-driven shallow water flows. Mathematics and Computers in Simulation, 99, 170-189. https://doi.org/10.1016/j.matcom.2013.04.016

A simple solver is proposed for the numerical solution of density-driven multi-layer shallow water flows. The governing equations consist on coupling the multi-layer shallow water equations for the hydraulic variables with suspended sediment transpor... Read More about A simple multi-layer finite volume solver for density-driven shallow water flows.

A fast finite volume solver for multi-layered shallow water flows with mass exchange (2014)
Journal Article
Audusse, E., Benkhaldoun, B., Sari, S., Seaid, M., & Tassi, P. (2014). A fast finite volume solver for multi-layered shallow water flows with mass exchange. Journal of Computational Physics, 272, 23-45. https://doi.org/10.1016/j.jcp.2014.04.026

A fast finite volume solver for hydrostatic multi-layered shallow water flows with mass exchange is investigated. In contrast to many models for multi-layered hydrostatic shallow water flows where the immiscible suppression is assumed, the present mo... Read More about A fast finite volume solver for multi-layered shallow water flows with mass exchange.

A new composite scheme for two-layer shallow water flows with shocks (2014)
Journal Article
Benkhaldoun, F., Izem, N., Sahmim, S., Seaid, M., & Wakrim, M. (2014). A new composite scheme for two-layer shallow water flows with shocks. Journal of Applied Mathematics and Computing, 44(1-2), 467-489. https://doi.org/10.1007/s12190-013-0703-z

This paper is devoted to solve the system of partial differential equations governing the flow of two superposed immiscible layers of shallow water flows. The system contains source terms due to bottom topography, wind stresses, and nonconservative p... Read More about A new composite scheme for two-layer shallow water flows with shocks.

An enriched finite element model with q-refinement for radiative boundary layers in glass cooling (2013)
Journal Article
Mohamed, M., Seaid, M., Trevelyan, J., & Laghrouche, O. (2014). An enriched finite element model with q-refinement for radiative boundary layers in glass cooling. Journal of Computational Physics, 258, 718-737. https://doi.org/10.1016/j.jcp.2013.11.005

Radiative cooling in glass manufacturing is simulated using the partition of unity finite element method. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary simplified P1 approximation... Read More about An enriched finite element model with q-refinement for radiative boundary layers in glass cooling.

Time-independent hybrid enrichment for finite element solution of transient conduction–radiation in diffusive grey media (2013)
Journal Article
Mohamed, M., Seaid, M., Trevelyan, J., & Laghrouche, O. (2013). Time-independent hybrid enrichment for finite element solution of transient conduction–radiation in diffusive grey media. Journal of Computational Physics, 251, 81-101. https://doi.org/10.1016/j.jcp.2013.05.030

We investigate the effectiveness of the partition-of-unity finite element method for transient conduction–radiation problems in diffusive grey media. The governing equations consist of a semi-linear transient heat equation for the temperature field a... Read More about Time-independent hybrid enrichment for finite element solution of transient conduction–radiation in diffusive grey media.

An unstructured finite-volume method for coupled models of suspended sediment and bed load transport in shallow-water flows (2013)
Journal Article
Benkhaldoun, F., Elmahi, I., Sari, S., & Seaid, M. (2013). An unstructured finite-volume method for coupled models of suspended sediment and bed load transport in shallow-water flows. International Journal for Numerical Methods in Fluids, 72(9), 967-993. https://doi.org/10.1002/fld.3771

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... Read More about An unstructured finite-volume method for coupled models of suspended sediment and bed load transport in shallow-water flows.

Assessment of coupling conditions in water way intersections (2013)
Journal Article
Herty, M., & Seaid, M. (2013). Assessment of coupling conditions in water way intersections. International Journal for Numerical Methods in Fluids, 71(11), 1438-1460. https://doi.org/10.1002/fld.3719

We present a numerical assessment of coupling conditions in T-junction for water flow in open canals. The mathematical model is based on the well-established shallow water equations for open channel flows. In the present work, the emphasis is given t... Read More about Assessment of coupling conditions in water way intersections.

A partition of unity FEM for time-dependent diffusion problems using multiple enrichment functions (2013)
Journal Article
Mohamed, M., Seaid, M., Trevelyan, J., & Laghrouche, O. (2013). A partition of unity FEM for time-dependent diffusion problems using multiple enrichment functions. International Journal for Numerical Methods in Engineering, 93(3), 245-265. https://doi.org/10.1002/nme.4383

An enriched partition of unity FEM is developed to solve time-dependent diffusion problems. In the present formulation, multiple exponential functions describing the spatial and temporal diffusion decay are embedded in the finite element approximatio... Read More about A partition of unity FEM for time-dependent diffusion problems using multiple enrichment functions.

A finite volume method for scalar conservation laws with stochastic time-space dependent flux function (2013)
Journal Article
Mohamed, K., Seaid, M., & Zahri, M. (2013). A finite volume method for scalar conservation laws with stochastic time-space dependent flux function. Journal of Computational and Applied Mathematics, 237(1), 614-632. https://doi.org/10.1016/j.cam.2012.07.014

We propose a new finite volume method for scalar conservation laws with stochastic time–space dependent flux functions. The stochastic effects appear in the flux function and can be interpreted as a random manner to localize the discontinuity in the... Read More about A finite volume method for scalar conservation laws with stochastic time-space dependent flux function.

Lattice Boltzmann simulation of free-surface temperature dispersion in shallow water flows. (2009)
Journal Article
Seaid, M., & Thömmes, G. (2009). Lattice Boltzmann simulation of free-surface temperature dispersion in shallow water flows. Advances in applied mathematics and mechanics, 1(3), 415-437

We develop a lattice Boltzmann method for modeling free-surface temperature dispersion in the shallow water flows. The governing equations are derived from the incompressible Navier-Stokes equations with assumptions of shallow water flows including b... Read More about Lattice Boltzmann simulation of free-surface temperature dispersion in shallow water flows..

Solving Wick-Stochastic Water Waves using a Galerkin Finite Element Method. (2009)
Journal Article
Manouzi, H., & Seaid, M. (2009). Solving Wick-Stochastic Water Waves using a Galerkin Finite Element Method. Mathematics and Computers in Simulation, 79(12), 3523-3533. https://doi.org/10.1016/j.matcom.2009.04.008

A Galerkin finite element approximation of Wick-stochastic water waves is developed and numerically investigated. The problems under study consist of a class of shallow water equations driven by white noise. Random effects may appear in the water fre... Read More about Solving Wick-Stochastic Water Waves using a Galerkin Finite Element Method..

Application of Mesh-Adaptation for Pollutant Transport by Water Flow. (2009)
Journal Article
Benkhaldoun, F., Elmahi, I., & Seaid, M. (2009). Application of Mesh-Adaptation for Pollutant Transport by Water Flow. Mathematics and Computers in Simulation, 79(12), 3415-3423. https://doi.org/10.1016/j.matcom.2009.04.007

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 where... Read More about Application of Mesh-Adaptation for Pollutant Transport by Water Flow..

Numerical Simulation of Stochastic Replicator Models in Catalyzed RNA-like Polymers. (2009)
Journal Article
Rößler, A., Seaid, M., & Zahri, M. (2009). Numerical Simulation of Stochastic Replicator Models in Catalyzed RNA-like Polymers. Mathematics and Computers in Simulation, 79(12), 3577-3586. https://doi.org/10.1016/j.matcom.2009.04.018

A stochastic model for replicators in catalyzed RNA-like polymers is presented and numerically solved. The model consists of a system of reaction–diffusion equations describing the evolution of a population formed by RNA-like molecules with catalytic... Read More about Numerical Simulation of Stochastic Replicator Models in Catalyzed RNA-like Polymers..

Large Eddy Simulation of Turbulent Heat Transport in the Strait of Gibraltar. (2009)
Journal Article
El-Amrani, M., & Seaid, M. (2009). Large Eddy Simulation of Turbulent Heat Transport in the Strait of Gibraltar. Mathematics and Computers in Simulation, 79(12), 3444-3454. https://doi.org/10.1016/j.matcom.2009.04.013

We develop a numerical model for large eddy simulation of turbulent heat transport in the Strait of Gibraltar. The flow equations are the incompressible Navier–Stokes equations including Coriolis forces and density variation through the Boussinesq ap... Read More about Large Eddy Simulation of Turbulent Heat Transport in the Strait of Gibraltar..

An Eulerian-Lagrangian Method for Coupled Parabolic-Hyperbolic Equations. (2009)
Journal Article
Seaid, M. (2009). An Eulerian-Lagrangian Method for Coupled Parabolic-Hyperbolic Equations. Applied Numerical Mathematics, 59(3-4), 754-768. https://doi.org/10.1016/j.apnum.2008.03.032

We present an Eulerian–Lagrangian method for the numerical solution of coupled parabolic-hyperbolic equations. The method combines advantages of the modified method of characteristics to accurately solve the hyperbolic equations with an Eulerian meth... Read More about An Eulerian-Lagrangian Method for Coupled Parabolic-Hyperbolic Equations..

A semi-Lagrangian method for a Fokker-Planck equation describing fiber dynamics (2009)
Journal Article
Klar, A., Reuterswärd, P., & Seaid, M. (2009). A semi-Lagrangian method for a Fokker-Planck equation describing fiber dynamics. Journal of Scientific Computing, 38(3), 349-367. https://doi.org/10.1007/s10915-008-9244-2

A simplified Fokker-Planck model for the lay-down of fibers on a conveyor belt in the production process of nonwovens is investigated. It takes into account the motion of the fiber under the influence of turbulence. The emphasis in this paper is on t... Read More about A semi-Lagrangian method for a Fokker-Planck equation describing fiber dynamics.

Simplified PN Models and Natural Convection-Radiation. (2008)
Presentation / Conference Contribution
Pinnau, R., & Seaid, M. (2008). Simplified PN Models and Natural Convection-Radiation. In L. L. Bonilla, M. Moscoso, G. Platero, & J. M. Vega (Eds.), Progress in Industrial Mathematics at ECMI 2006 (397-401)

Validation of simplified PN models for radiative transfer in combustion. (2008)
Journal Article
Schneider, E., Seaid, M., Janicka, J., & Klar, A. (2008). Validation of simplified PN models for radiative transfer in combustion. Communications in numerical methods in engineering, 24(2), 85-96. https://doi.org/10.1002/cnm.941

This paper illustrates the use of simplified PN approximations as a tools of achieving verification of codes and simulations of radiative transfer in combustion systems. The main advantage of considering these models is the fact that the integro-diff... Read More about Validation of simplified PN models for radiative transfer in combustion..

Extension of weakly compressible approximations to incompressible thermal flows. (2008)
Journal Article
El-Amrani, M., & Seaid, M. (2008). Extension of weakly compressible approximations to incompressible thermal flows. Communications in numerical methods in engineering, 24(1), 33 - 48. https://doi.org/10.1002/cnm.954

Weakly compressible and advection approximations of incompressible isothermal flows were developed and tested in (Commun. Numer. Methods Eng. 2006; 22:831-847). In this paper, we extend the method to solve equations governing incompressible thermal f... Read More about Extension of weakly compressible approximations to incompressible thermal flows..

Large-Eddy Simulation of Thermal Flows based on Discrete-Velocity Models. (2008)
Journal Article
Banda, M., Seaid, M., & Teleaga, I. (2008). Large-Eddy Simulation of Thermal Flows based on Discrete-Velocity Models. SIAM Journal on Scientific Computing, 30(4), 1756-1777. https://doi.org/10.1137/070682174

We derive a Godunov-type relaxation scheme for turbulent flows with heat transfer. The building block of this approach is a kinetic Boltzmann-type formulation for a model of turbulent thermal flows based on large-eddy simulation modeling. Discrete-ve... Read More about Large-Eddy Simulation of Thermal Flows based on Discrete-Velocity Models..

A finite element modified method of characteristics for convective heat transport (2008)
Journal Article
El-Amrani, M., & Seaid, M. (2008). A finite element modified method of characteristics for convective heat transport. Numerical Methods for Partial Differential Equations, 24(3), 776 - 798. https://doi.org/10.1002/num.20288

We propose a finite element modified method of characteristics for numerical solution of convective heat transport. The flow equations are the incompressible Navier-Stokes equations including density variation through the Boussinesq approximation. Th... Read More about A finite element modified method of characteristics for convective heat transport.

Finite Element P1 Solution of Thermal Flow past a Circular Cylinder with Radiation. (2008)
Journal Article
Seaid, M., & El-Amrani, M. (2008). Finite Element P1 Solution of Thermal Flow past a Circular Cylinder with Radiation. International Journal of Computer Mathematics, 85(3-4), 641-656. https://doi.org/10.1080/00207160601167060

We propose a finite element method for solving combined convection and radiation in laminar flow past a circular cylinder. The flow problem is described by the thermal incompressible Navier-Stokes equations subject to a Boussinesq approach. To incorp... Read More about Finite Element P1 Solution of Thermal Flow past a Circular Cylinder with Radiation..

Simulation of transient gas flow at pipe-to-pipe intersections. (2008)
Journal Article
Herty, M., & Seaid, M. (2008). Simulation of transient gas flow at pipe-to-pipe intersections. International Journal for Numerical Methods in Fluids, 56(5), 485 - 506. https://doi.org/10.1002/fld.1531

We numerically investigate a well-established mathematical model for gas flow in pipeline networks. The emphasis is given to the description of coupling conditions at pipe-to-pipe intersections. The accurate prediction of these coupling conditions is... Read More about Simulation of transient gas flow at pipe-to-pipe intersections..

Lattice Boltzmann Simulation of Depth-Averaged Models in Flow Hydraulics. (2008)
Journal Article
Klar, A. S., & M. Thoemmes, G. (2008). Lattice Boltzmann Simulation of Depth-Averaged Models in Flow Hydraulics. International Journal of Computational Fluid Dynamics, 22(7), 507 - 522. https://doi.org/10.1080/10618560802243838

We apply a lattice Boltzmann method (LBM) for the simulation of depth-averaged models in flow hydraulics and dispersion of pollutants. The mathematical equations for these models can be obtained from the incompressible Navier-Stokes equations under t... Read More about Lattice Boltzmann Simulation of Depth-Averaged Models in Flow Hydraulics..

Coupled finite element–lattice Boltzmann analysis (2008)
Journal Article
Haslam, I., Crouch, R., & Seaïd, M. (2008). Coupled finite element–lattice Boltzmann analysis. Computer Methods in Applied Mechanics and Engineering, 197(51-52), 4505-4511. https://doi.org/10.1016/j.cma.2008.04.002

A coupled finite element (FE) and lattice Boltzmann (LB) numerical scheme to model the deformation of a porous solid through which fluid flows could offer an attractive solution strategy. As a precursor to a complete simulator, we review the two meth... Read More about Coupled finite element–lattice Boltzmann analysis.

A Galerkin-Characteristic Method for Large-Eddy Simulation of Turbulent Flow and Heat Transfer (2008)
Journal Article
El-Amrani, M., & Seaid, M. (2008). A Galerkin-Characteristic Method for Large-Eddy Simulation of Turbulent Flow and Heat Transfer. SIAM Journal on Scientific Computing, 30(6), 2734-2754. https://doi.org/10.1137/080720711

This work aims at the development of a nonoscillatory Galerkin-characteristic method for large-eddy simulation of turbulent flow and heat transfer. The method is based on combining the modified method of characteristics with a Galerkin finite element... Read More about A Galerkin-Characteristic Method for Large-Eddy Simulation of Turbulent Flow and Heat Transfer.

Simplified radiative models for low-Mach number reactive flows. (2008)
Journal Article
Teleaga, I., & Seaid, M. (2008). Simplified radiative models for low-Mach number reactive flows. Applied Mathematical Modelling, 32(6), 971-991. https://doi.org/10.1016/j.apm.2007.02.021

We introduce a class of numerical models for the simulation of radiative effects in low-Mach number reactive flows. These models are based on simplified PN approximations for radiative heat transfer, low-Mach asymptotic in the compressible flow, and... Read More about Simplified radiative models for low-Mach number reactive flows..

Incompressible Navier-Stokes equation solvers based on lattice Boltzmann relaxation systems. (2008)
Presentation / Conference Contribution
Banda, M., Seaid, M., & Teleaga, I. (2008). Incompressible Navier-Stokes equation solvers based on lattice Boltzmann relaxation systems. In Special Issue:Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, Zürich 2007 (2100001-2100002). https://doi.org/10.1002/pamm.200700010

In this talk some recent numerical results based on discrete-velocity relaxation systems will be presented. Discrete-velocity equations are derived from continuous Boltzmann-type equations with appropriate approximations suitable for incompressible f... Read More about Incompressible Navier-Stokes equation solvers based on lattice Boltzmann relaxation systems..

Lattice Boltzmann Methods for Shallow Water Flow Applications (2007)
Journal Article
Thömmes, G., Seaid, M., & Banda, M. (2007). Lattice Boltzmann Methods for Shallow Water Flow Applications. International Journal for Numerical Methods in Fluids, 55(7), 673-692. https://doi.org/10.1002/fld.1489

We apply the lattice Boltzmann (LB) method for solving the shallow water equations with source terms such as the bed slope and bed friction. Our aim is to use a simple and accurate representation of the source terms in order to simulate practical sha... Read More about Lattice Boltzmann Methods for Shallow Water Flow Applications.

Well-Balanced Finite Volume Schemes for Pollutant Transport by Shallow Water Equations on Unstructured Meshes (2007)
Journal Article
Benkhaldoun, F., Elmahi, I., & Seaid, M. (2007). Well-Balanced Finite Volume Schemes for Pollutant Transport by Shallow Water Equations on Unstructured Meshes. Journal of Computational Physics, 226(1), 180-203. https://doi.org/10.1016/j.jcp.2007.04.005

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 resolu... Read More about Well-Balanced Finite Volume Schemes for Pollutant Transport by Shallow Water Equations on Unstructured Meshes.

A Consistent Approach for the Coupling of Radiation and Hydrodynamics at Low Mach Number (2007)
Journal Article
Dubroca, B., Seaid, M., & Teleaga, I. (2007). A Consistent Approach for the Coupling of Radiation and Hydrodynamics at Low Mach Number. Journal of Computational Physics, 225(1), 1039-1065. https://doi.org/10.1016/j.jcp.2007.01.011

We present a consistent numerical model for coupling radiation to hydrodynamics at low Mach number. The hydrodynamical model is based on a low-Mach asymptotic in the compressible flow that removes acoustic wave propagation while retaining the compres... Read More about A Consistent Approach for the Coupling of Radiation and Hydrodynamics at Low Mach Number.

Numerical Simulation of Natural and Mixed Convection Flows by Galerkin-Characteristic Method (2007)
Journal Article
El-Amrani, M., & Seaid, M. (2007). Numerical Simulation of Natural and Mixed Convection Flows by Galerkin-Characteristic Method. International Journal for Numerical Methods in Fluids, 53(12), 1819-1845. https://doi.org/10.1002/fld.1384

A numerical investigation is performed to study the solution of natural and mixed convection flows by Galerkin-characteristic method. The method is based on combining the modified method of characteristics with a Galerkin finite element discretizatio... Read More about Numerical Simulation of Natural and Mixed Convection Flows by Galerkin-Characteristic Method.

Animating Water Waves Using Semi-Lagrangian Techniques. (2005)
Presentation / Conference Contribution
El-Amrani, M., & Seaid, M. (2005). Animating Water Waves Using Semi-Lagrangian Techniques. In A. . D. Bucchianico, R. M. M. Mattheij, & M. A. Peletier (Eds.), Progress in Industrial Mathematics at ECMI 2004 (494-498)

A New Monte Carlo Approach for Conservation Laws and Relaxation Systems. (2004)
Presentation / Conference Contribution
Pareschi, L., & Seaid, M. (2004, December). A New Monte Carlo Approach for Conservation Laws and Relaxation Systems

We present a Monte Carlo method for approximating the solution of conservation laws. A relaxation method is used to transform the conservation law to a kinetic form that can be interpreted in a probabilistic manner. A Monte Carlo algorithm is then us... Read More about A New Monte Carlo Approach for Conservation Laws and Relaxation Systems..