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Pre-Publicación 2016-39

Raimund Bürger, Stefan Diehl, María Carmen Martí, Pep Mulet, Ingmar Nopens, Elena Torfs, Peter Vanrolleghem:

Numerical solution of a multi-class model for batch settling in water resource recovery facilities

Abstract:

In [E. Torfs et al., Water Sci. Technol., in press] a new uni ed framework to model settling tanks in water resource recovery facilities was proposed providing a set of partial di fferential equations (PDEs) modelling di fferent settling unit processes in wastewater treatment such as primary and secondary settling tanks (PSTs and SSTs). The extension to a multi-class framework to deal with the distributed properties of the settling particles leads to a system of nonlinear hyperbolic-parabolic PDEs whose solutions may contain really sharp transitions. This necessitates the use of a consistent and robust numerical method to obtain well-resolved and reliable approximations to the PDE solutions. The use of implicit-explicit Runge-Kutta (IMEX-RK) schemes, along with the weighted essentially non-oscillatory (WENO) shock-capturing technology for the discretization of the set of equations, is advocated in this work. The versatility of the proposed uni ed framework is demonstrated through a set of numerical examples for batch settling occuring in both PSTs and SSTs, along with the efficiency and reliability of the numerical scheme.

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