Random walks with negative particles for discontinuous diffusion and porosity

Hamza Oukili (1) , Rachid Ababou (1) , Gerald Debenest (1) , B. Noetinger (2)

1 IMFT - Institut de mécanique des fluides de Toulouse
2 IFPEN - IFP Energies nouvelles

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 or porosity. 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.

Mots clés: Diffusion; Random Walk Particle Tracking (RWPT) -Discontinuities; Analytical solutions; Porous materials; Negative particles

Domaines: Mécanique des fluides [physics.class-ph]

Hamza Oukili, Rachid Ababou, Gerald Debenest, B. Noetinger. Random walks with negative particles for discontinuous diffusion and porosity. Journal of Computational Physics, 2019, 396, pp.687-701. ⟨10.1016/j.jcp.2019.07.006⟩. ⟨hal-02409018⟩