Anthony Beaudoin

A parallel scientific software for heterogeneous hydrogeoloy

Numerical modelling is an important key for the management and remediation of groundwater resources [28]. As opposed to surface water and to highly karstic geologies, groundwater does not flow in well-identified open streams but is like water flowing in the voids of a sponge. Groundwater is highly dependent on the percentage of pores (porosity), size and connectivity of the pores that controls the permeability of the medium. Its quality depends on the biochemical reactivity of the crossed geological media and on the kinetics of the biochemical reactions. These parameters (porosity, permeability, reactivity) are highly variable. Several field experiments show that the natural geological formations are highly heterogeneous, leading to preferential flow paths and stagnant regions. The contaminant migration is strongly affected by these irregular water velocity distributions. Transport of contaminant by advection and dispersion induce a large spreading of the particles generally called plume. The characterization of the plume remains a much debated topic [7,16,25]. Fractures and heterogeneous sedimentary units cannot be identified whatever the remote data, whether geophysical, geological or hydraulic. Because data give a rather scarce description of the medium hydraulic properties, predictions rely heavily on numerical modelling. Numerical modelling should integrate the multi-scale geological heterogeneity, simulate the hydraulic flow and transport phenomena and quantify uncertainty coming from the lack of data. Analytical techniques like homogenization or perturbations are in general not relevant. Modelling must thus be performed in a probabilistic framework that transfers the lack of data on prediction variability [1]. Practically, random studies require running a large number of simulations, for two reasons. First, non intrusive Uncertainty Quantification methods rely on sampling of data. Second, the questions addressed must consider a large panel of parameters (Peclet number, variance of probabilistic models, etc). The hydraulic simulations must be performed on domains of a large size, at the scale of management of the groundwater resource or at the scale of the homogeneous medium type in terms of geology. This domain must be discretized at a fine resolution to take into account the scale of geological heterogeneities. Also, large time ranges must be considered in order to determine an asymptotic behaviour. High performance computing is thus necessary to carry out these large scale simulations.

Simulation of anisotropic diffusion by means of a diffusion velocity method

An alternative method to the Particle Strength Exchange method for solving the advection-diffusion equation in the general case of a non-isotropic and non-uniform diffusion is proposed. This method is an extension of the diffusion velocity method. It is shown that this extension is quite straightforward due to the explicit use of the diffusion flux in the expression of the diffusion velocity. This approach is used to simulate pollutant transport in groundwater and the results are compared to those of the PSE method presented in an earlier study by Zimmermann et al.

An efficient parallel particle tracker for advection-diffusion simulations in heterogeneous porous media

The heterogeneity of natural geological formations has a major impact in the contamination of groundwater by migration of pollutants. In order to get an asymptotic behavior of the solute dispersion, numerical simultations require large scale computations. We have developed a fully parallel software, where the transport model is an original parallel particke tracker. Our performance results on a distributed memory parallel architecture show the efficiency of our algorithm, for the whole range of geological parameters studied.

From Navier-Stokes to Stokes by means of particle methods

The viscous flow around a circular cylinder was investigated by means of a particle method over a wide Reynolds number range, from 0.0001 to 1000. A special care was devoted to the satisfaction of the no-slip condition which was expressed through a fourth order partial differential equation for the stream function according to the method initially proposed by Achdou and Pironneau. This equation was solved by a boundary integral method which simultaneously satisfied a Dirichlet and a Neumann condition. The algorithm was immersed within a particle method framework and results in a versatile method which can deal with relatively high Reynolds numbers as well as Stokes flows. The numerical results were analysed and compared to those obtained by others numerically, experimentally and even theoretically for the low Reynolds number limit. The behaviour of the method for the two extreme cases was specially investigated.

Modeling reactive transport in heterogeneous saturated porous media: Effects of nonlinear sorption

ABSTRACT The present study is devoted to the simulation of nonlinear sorbing plume transport in homogeneous and heterogeneous saturated porous media. This study was performed by means of Monte Carlo simulations. For each Monte Carlo simulation, two problems have to be resolved. For the flow problem, the mass conservation equation, coupled with Darcys law, is solved on a regular grid by means of a finite volume method. For the transport problem, the advection—dispersion equation is solved by means of a particles method. This langrangian method is based on a discretization of concentration field with particles defined by a location and a weight. At each time step, the transport problem is then resolved by evaluating the new location and weight of particles.