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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.