Implementation of Anisotropic Diffusivity in a 2D Shallow Water Pollutant Transport Model

Abstract

This thesis investigates the modelling of pollutant transport in flooded urban environments using a two-dimensional shallow water advection-diffusion framework. The numerical model is based on a finite-volume discretization and incorporates both isotropic and anisotropic diffusion tensors. A particular focus is placed on distinguishing between longitudinal and transverse diffusion, and evaluating their respective influence on the simulated pollutant spreading. The advection term is discretized using various numerical schemes, including a first-order upwind method and a second-order flux-limited scheme. Their impact on accuracy and numerical diffusion is assessed through benchmark tests involving analytical solutions. The model is then applied to replicate experimental scenarios from the M.U.R.I. platform at INRAE (Lyon), using both time-averaged and fully unsteady hydrodynamic fields generated by the Wolf 2D model. A sensitivity analysis is performed across a wide range of anisotropic diffusion coefficients. Results show that the longitudinal coefficient has a predominant influence on the downstream elongation of the pollutant plume, while the transverse component contributes to lateral dispersion. The spatial structure of the concentration field results from the combined effect of both coefficients, depending on the flow configuration and injection point. Although no universal relationship is observed, the anisotropy ratio between both longitudinal and transverse coefficient provides a useful metric to compare different configurations. For each test case, a ratio between 2.5 and 3.5 is typically associated with the best agreement with experimental data, reflecting the directional nature of pollutant transport in urban environments. The study highlights the importance of both anisotropic calibration and the use of time-resolved hydrodynamics for accurately capturing pollutant dynamics in complex urban flows. It also underscores the trade-offs between numerical cost and physical realism, motivating future developments aimed at accelerating simulations and extending validation to additional configurations and injection points.