Hamza Oukili

(Journal-) Articles

1. Oukili, H., Ababou, R., Debenest, G., & Noetinger, B. (2021). Multi-scale study of diffusion in composite grain–pore systems based on particles random walk. Comptes Rendus. Mécanique, 349(3), Article 3. https://doi.org/10.5802/crmeca.94
   • Abstract
   • BibTeX
   • Link

   Abstract

   This paper studies diffusion processes at different scales in two-dimensional (2D) composite media (grain-pore porous micromodels). To model diffusion, this study uses the random walk particle tracking (RWPT) method based on 2D analytical solutions in finite and semi-infinite domains with zero-flux boundary conditions (BC) at grain boundaries. The analytical solutions are developed using a method of images. Then, an RWPT combined to a Stop&Go algorithm is derived from these analytical solutions. The developed RWPT algorithm is then used to model diffusion processes inside the pores at the "microscopic" level (microscale), while the grain elements are assumed inaccessible to diffusion (zero-flux BC condition at the interface grain/pore). The composite medium, where the diffusion occurs, is a numerical micromodel made of periodic motifs of rectangular grains. Particles are initially located at the center of a pore, and diffuses in the periodic motifs micromodel (infinite domain). First, the grains are chosen square with different sizes to vary the porosity. Second, for constant porosities, the grains are elongated to study the effect of the anisotropy ratio on diffusion processes. Effective macroscale properties (porosities, effective diffusion tensors, tortuosities) are then calculated using moments of particles positions. The results obtained fit well with theoretical expectations and are in very good agreement with results found in the literature.

   BibTeX

   @article{CRMECA_2021__349_3_529_0, abstract = {This paper studies diffusion processes at different scales in two-dimensional (2D) composite media (grain-pore porous micromodels). To model diffusion, this study uses the random walk particle tracking (RWPT) method based on 2D analytical solutions in finite and semi-infinite domains with zero-flux boundary conditions (BC) at grain boundaries. The analytical solutions are developed using a method of images. Then, an RWPT combined to a Stop&Go algorithm is derived from these analytical solutions. The developed RWPT algorithm is then used to model diffusion processes inside the pores at the "microscopic" level (microscale), while the grain elements are assumed inaccessible to diffusion (zero-flux BC condition at the interface grain/pore). The composite medium, where the diffusion occurs, is a numerical micromodel made of periodic motifs of rectangular grains. Particles are initially located at the center of a pore, and diffuses in the periodic motifs micromodel (infinite domain). First, the grains are chosen square with different sizes to vary the porosity. Second, for constant porosities, the grains are elongated to study the effect of the anisotropy ratio on diffusion processes. Effective macroscale properties (porosities, effective diffusion tensors, tortuosities) are then calculated using moments of particles positions. The results obtained fit well with theoretical expectations and are in very good agreement with results found in the literature.}, author = {Oukili, Hamza and Ababou, Rachid and Debenest, G\'erald and Noetinger, Beno{\^\i}t}, doi = {10.5802/crmeca.94}, journal = {Comptes Rendus. M\'ecanique}, language = {en}, number = 3, pages = {529--558}, publisher = {Acad\'emie des sciences, Paris}, title = {Multi-scale study of diffusion in composite grain{\textendash}pore systems based on particles random walk}, url = {https://doi.org/10.5802/crmeca.94}, volume = 349, year = 2021 }

   Link

   https://doi.org/10.5802/crmeca.94
2. Oukili, H., Ababou, R., Debenest, G., & Noetinger, B. (2019). Random Walks with negative particles for discontinuous diffusion and porosity. Journal of Computational Physics, 396, 687–701. https://doi.org/10.1016/j.jcp.2019.07.006
   • Abstract
   • BibTeX
   • Link

   Abstract

   This study develops a new Lagrangian particle method for modeling flow and transport phenomena in complex porous media with discontinuities. For instance, diffusion processes can be modeled by Lagrangian Random Walk algorithms. However, discontinuities and heterogeneities are difficult to treat, particularly discontinuous diffusion D(x) or porosity θ(x). In the literature on particle Random Walks, previous methods used to handle this discontinuity problem can be characterized into two main classes as follows: "Interpolation techniques", and "Partial reflection methods". One of the main drawbacks of these methods is the small time step required in order to converge to the expected solution, particularly in the presence of many interfaces. These restrictions on the time step, lead to inefficient algorithms. The Random Walk Particle Tracking (RWPT) algorithm proposed here is, like others in the literature, discrete in time and continuous in space (gridless). We propose a novel approach to partial reflection schemes without restrictions on time step size. The new RWPT algorithm is based on an adaptive "Stop&Go" time-stepping, combined with partial reflection/refraction schemes, and extended with a new concept of negative mass particles. To test the new RWPT scheme, we develop analytical and semi-analytical solutions for diffusion in the presence of multiple interfaces (discontinuous multi-layered medium). The results show that the proposed Stop&Go RWPT scheme (with adaptive negative mass particles) fits extremely well the semi-analytical solutions, even for very high contrasts and in the neighborhood of interfaces. The scheme provides a correct diffusive solution in only a few macro-time steps, with a precision that does not depend on their size.

   BibTeX

   @article{OUKILI2019687, abstract = {This study develops a new Lagrangian particle method for modeling flow and transport phenomena in complex porous media with discontinuities. For instance, diffusion processes can be modeled by Lagrangian Random Walk algorithms. However, discontinuities and heterogeneities are difficult to treat, particularly discontinuous diffusion D(x) or porosity θ(x). In the literature on particle Random Walks, previous methods used to handle this discontinuity problem can be characterized into two main classes as follows: "Interpolation techniques", and "Partial reflection methods". One of the main drawbacks of these methods is the small time step required in order to converge to the expected solution, particularly in the presence of many interfaces. These restrictions on the time step, lead to inefficient algorithms. The Random Walk Particle Tracking (RWPT) algorithm proposed here is, like others in the literature, discrete in time and continuous in space (gridless). We propose a novel approach to partial reflection schemes without restrictions on time step size. The new RWPT algorithm is based on an adaptive "Stop&Go" time-stepping, combined with partial reflection/refraction schemes, and extended with a new concept of negative mass particles. To test the new RWPT scheme, we develop analytical and semi-analytical solutions for diffusion in the presence of multiple interfaces (discontinuous multi-layered medium). The results show that the proposed Stop&Go RWPT scheme (with adaptive negative mass particles) fits extremely well the semi-analytical solutions, even for very high contrasts and in the neighborhood of interfaces. The scheme provides a correct diffusive solution in only a few macro-time steps, with a precision that does not depend on their size.}, author = {Oukili, H. and Ababou, R. and Debenest, G. and Noetinger, B.}, doi = {https://doi.org/10.1016/j.jcp.2019.07.006}, issn = {0021-9991}, journal = {Journal of Computational Physics}, pages = {687-701}, title = {Random Walks with negative particles for discontinuous diffusion and porosity}, url = {https://www.sciencedirect.com/science/article/pii/S0021999119304917}, volume = 396, year = 2019 }

   Link

   https://www.sciencedirect.com/science/article/pii/S0021999119304917