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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.