6533b862fe1ef96bd12c6132
RESEARCH PRODUCT
Numerical solution of a multi-class model for batch settling in water resource recovery facilities
M. Carmen MartíStefan DiehlIngmar NopensElena TorfsRaimund BürgerPep MuletPeter A. Vanrolleghemsubject
Mathematical optimizationPartial differential equationDiscretizationApplied MathematicsReliability (computer networking)Numerical analysisRelaxation (iterative method)010103 numerical & computational mathematics01 natural sciences6. Clean water010101 applied mathematicsSet (abstract data type)SettlingModeling and Simulation0101 mathematicsConvection–diffusion equationMathematicsdescription
In Torfs et al. (2017) a new unified 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 non-linear hyperbolic-parabolic PDEs whose solutions may contain very 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 unified framework is demonstrated through a set of numerical examples for batch settling occurring in both PSTs and SSTs, along with the efficiency and reliability of the numerical scheme.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-09-01 | Applied Mathematical Modelling |