Fast reliable simulations of secondary settling tanks in wastewater treatment with semi-implicit time discretization

The bio-kinetic and sedimentation processes of wastewater treatment plants can be modelled by a large system of coupled nonlinear ordinary and partial differential equations (ODEs and PDEs). The subprocess of continuous sedimentation, which contains concentration discontinuities, is modelled by a degenerate parabolic conservation PDE with spatially discontinuous coefficients. A spatial discretization of this PDE described in Bürger et al. (2013) results in a large system of method-of-lines ODEs for the entire plant and simulation can be performed by integration in time. In practice, standard time integration methods available in commercial simulators are often used. Shortages of such methods are here shown, such as the smearing of shock waves by Runge-Kutta methods and long execution times. A semi-implicit time discretization, which is described in detail, provides substantially shorter computational times and is more efficient than standard methods.