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
In [E. Torfs et al., Water Sci. Technol., in press] a new unied framework to model settling tanks in water resource recovery facilities was proposed providing a set of partial differential equations (PDEs) modelling different 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 unied 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.
This preprint gave rise to the following definitive publication(s):
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. Applied Mathematical Modelling, vol. 49, pp. 415-436, (2017).