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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.