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A Galerkin-Characteristic Finite Element Method for Three-Dimensional Convection-Dominated Problems (2021)
Journal Article
Khouya, B., El-Amrani, M., & Seaid, M. (2021). A Galerkin-Characteristic Finite Element Method for Three-Dimensional Convection-Dominated Problems. Advances in applied mathematics and mechanics, 13(3), 503-526. https://doi.org/10.4208/aamm.oa-2020-0105

We present an efficient Galerkin-characteristic finite element method for the numerical solution of convection-diffusion problems in three space dimensions. The modified method of characteristics is used to discretize the convective term in a finite... Read More about A Galerkin-Characteristic Finite Element Method for Three-Dimensional Convection-Dominated Problems.

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. (2021). A Computational Model for Simulation of Shallow Water Waves by Elastic Deformations in the Topography. Communications in computational physics, 29(4), 1095–1124. 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.