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

摘要

We consider a coupled PDE-ODE model governing the bacterial dynamics of the anaerobic biodegradation of household waste in a landfill. The biological activity, represented with a non linear system of ordinary differential equations (ODE), takes place in an unsaturated porous medium represented by Darcy law. We transform the initial system of equations into a fully PDE model where the bacterial distribution is spatialized as reaction-diffusion equations. We carry out the mathematical and numerical analysis of the new model and its discrete counterpart in a variational framework. Using mixed finite elements approximation for the nonlinear Darcy flow and standard finite elements to solve the reaction-diffusion system, we perform several numerical simulations in 2D and 3D in agreement with the theoretical results.