Continuously operated settling tanks are used for the gravity separation of solid-liquid suspensions in several industries. Mathematical models of these units form a topic for well-posedness and numerical analysis even in one space dimension due to the spatially discontinuous coefficients of the underlying strongly degenerate parabolic, nonlinear model partial differential equation (PDE). Such a model is extended to describe the sedimentation of multi-component particles that react with several soluble components of the liquid phase. The fundamental balance equations contain the mass percentages of the components of the solid and liquid phases. The equations are reformulated as a system of nonlinear PDEs that can be solved consecutively in each time step by an explicit numerical scheme. This scheme combines a difference scheme for conservation laws with discontinuous flux with an approach of numerical percentage propagation for multi-component flows. The main result is an invariant-region property, which implies that physically relevant numerical solutions are produced. Simulations of denitrification in secondary settling tanks in wastewater treatment illustrate the model and its discretization.
Accepté le :
DOI : 10.1051/m2an/2017038
Mots clés : clarifier-thickener, invariant-region property, multi-component flow, percentage propagation, wastewater treatment
@article{M2AN_2018__52_2_365_0,
author = {B\"urger, Raimund and Diehl, Stefan and Mej{\'\i}as, Camilo},
title = {A difference scheme for a degenerating convection-diffusion-reaction system modelling continuous sedimentation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {365--392},
publisher = {EDP-Sciences},
volume = {52},
number = {2},
year = {2018},
doi = {10.1051/m2an/2017038},
zbl = {1412.65068},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2017038/}
}
TY - JOUR AU - Bürger, Raimund AU - Diehl, Stefan AU - Mejías, Camilo TI - A difference scheme for a degenerating convection-diffusion-reaction system modelling continuous sedimentation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2018 SP - 365 EP - 392 VL - 52 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2017038/ DO - 10.1051/m2an/2017038 LA - en ID - M2AN_2018__52_2_365_0 ER -
%0 Journal Article %A Bürger, Raimund %A Diehl, Stefan %A Mejías, Camilo %T A difference scheme for a degenerating convection-diffusion-reaction system modelling continuous sedimentation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2018 %P 365-392 %V 52 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2017038/ %R 10.1051/m2an/2017038 %G en %F M2AN_2018__52_2_365_0
Bürger, Raimund; Diehl, Stefan; Mejías, Camilo. A difference scheme for a degenerating convection-diffusion-reaction system modelling continuous sedimentation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 2, pp. 365-392. doi : 10.1051/m2an/2017038. http://www.numdam.org/articles/10.1051/m2an/2017038/
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