Preprint 2012-03
Raimund Bürger, Stefan Diehl, Sebastian Farås, Ingmar Nopens, Elena Torfs:
A consistent modelling methodology for secondary settling tanks: A reliable numerical method
Abstract:
The Consistent Modelling Methodology (CMM) for Secondary Settling Tanks(SSTs) [Bürger, Diehl and Nopens, Water Res. 45 (2011) 247{2260] leads to a partial diff erential equation (PDE) of non-linear convection-dif usion type for the solids concentration as a function of depth and time. The model PDE includes a flux that depends discontinuously on spatial position modelling hindered settling and bulk flows, a singular source term describing the feed mechanism, a degenerating term accounting for sediment compressibility, and a dispersion term for the turbulence around the feed inlet. In addition, the solution itself is discontinuous. A consistent, reliable and robust numerical method that properly handles these difficulties is derived and presented in detail. Many constitutive relations for hindered settling, compression and dispersion can be used within the model, allowing the user to switch on and o f e ffects of interest. The method is based on a sound layer-wise spatial discretization and a method-of-lines formulation, which eventually gives rise to a fully discrete numerical scheme. Simulations show the eff ect of the dispersion term on effluent suspended solids and total sludge mass in the SST.
This preprint gave rise to the following definitive publication(s):
Raimund BüRGER, Stefan DIEHL, Sebastian FARåS, Ingmar NOPENS, Elena TORFS: A consistent modelling methodology for secondary settling tanks: A reliable numerical method. Water Science and Technology, vol. 68, 1, pp. 192-208, (2013).