On reliable and unreliable numerical methods for the simulation of secondary settling tanks in wastewater treatment

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On reliable and unreliable numerical methods for the simulation of secondary settling tanks in wastewater treatment. / Bürger, Raimund; Diehl, Stefan; Farås, Sebastian; Nopens, Ingmar.

In: Computers & Chemical Engineering, Vol. 41, 2012, p. 93-105.

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TY - JOUR

T1 - On reliable and unreliable numerical methods for the simulation of secondary settling tanks in wastewater treatment

AU - Bürger, Raimund

AU - Diehl, Stefan

AU - Farås, Sebastian

AU - Nopens, Ingmar

PY - 2012

Y1 - 2012

N2 - Abstract in Undetermined A one-dimensional model for the sedimentation-compression-dispersion process in the secondary settling tank can be expressed as a nonlinear strongly degenerate parabolic partial differential equation (PDE), which has coefficients with spatial discontinuities. Reliable numerical methods for simulation produce approximate solutions that converge to the physically relevant solution of the PDE as the discretization is refined. We focus on two such methods and assess their performance via simulations for two scenarios. One method is provably convergent and is used as a reference method. The other method is less efficient in reducing numerical errors, but faster and more easily implemented. Furthermore, we demonstrate some pitfalls when deriving numerical methods for this type of PDE and can thereby rule out certain methods as unsuitable; among others, the wide-spread Takacs method. (c) 2012 Elsevier Ltd. All rights reserved.

AB - Abstract in Undetermined A one-dimensional model for the sedimentation-compression-dispersion process in the secondary settling tank can be expressed as a nonlinear strongly degenerate parabolic partial differential equation (PDE), which has coefficients with spatial discontinuities. Reliable numerical methods for simulation produce approximate solutions that converge to the physically relevant solution of the PDE as the discretization is refined. We focus on two such methods and assess their performance via simulations for two scenarios. One method is provably convergent and is used as a reference method. The other method is less efficient in reducing numerical errors, but faster and more easily implemented. Furthermore, we demonstrate some pitfalls when deriving numerical methods for this type of PDE and can thereby rule out certain methods as unsuitable; among others, the wide-spread Takacs method. (c) 2012 Elsevier Ltd. All rights reserved.

KW - Secondary settling tank

KW - Wastewater treatment plant

KW - Method of lines

KW - Godunov flux

KW - Numerical method

KW - Efficiency

U2 - 10.1016/j.compchemeng.2012.02.016

DO - 10.1016/j.compchemeng.2012.02.016

M3 - Article

VL - 41

SP - 93

EP - 105

JO - Computers and Chemical Engineering

T2 - Computers and Chemical Engineering

JF - Computers and Chemical Engineering

SN - 1873-4375

ER -