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Pré-Publication, Document De Travail Année : 2020

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

Résumé

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.
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Dates et versions

hal-02455294 , version 1 (25-01-2020)

Identifiants

  • HAL Id : hal-02455294 , version 1

Citer

Zakaria Belhachmi, Zoubida Mghazli, Salih Ouchtout. Mathematical modelling and numerical approximation of a leachate flow in the anaerobic biodegradation of waste in a landfill. 2020. ⟨hal-02455294⟩

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