Mathematical modelling and numerical approximation of a leachate flow in the anaerobic biodegradation of waste in a landfill

Abstract

We consider a coupled PDE-ODEs model that describes the bacterial dynamics of the anaerobic biodegradation of waste in a landfill taken as an unsatureted porous medium. We add a diffusion term in the ODEs part which gives a rise to a reaction-diffusion system coupled with porous media equations. This yields a new model of the biodegradation of the waste where the biological variables are varying in space and time. We perform the mathematical analysis of the resulting system and we consider a discretization based on BDF schemes and P1 conforming finite elements for the reaction-diffusion subsystem and a mixed finite elements RT0 /P0 for the Darcy flow. We carry out the numerical analysis and we obtain the expected a priori estimates. We perform several numerical 2D and 3D simulations which are in agreement with the theoretical results