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

Abstract 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.

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