On reliable and unreliable numerical methods for the simulation of secondary settling tanks in wastewater treatment

A one-dimensional model for the sedimentation-compression-dispersion process in the secondary settling tank can be expressed as a nonlinear strongly degenerate parabolic partial differential equation (PDE), which has coefficients with spatial discontinuities. Reliable numerical methods for simulation produce approximate solutions that converge to the physically relevant solution of the PDE as the discretization is refined. We focus on two such methods and assess their performance via simulations for two scenarios. One method is provably convergent and is used as a reference method. The other method is less efficient in reducing numerical errors, but faster and more easily implemented. Furthermore, we demonstrate some pitfalls when deriving numerical methods for this type of PDE and can thereby rule out certain methods as unsuitable; among others, the wide-spread Takács method.

► A one-dimensional model for the sedimentation-compression-dispersion process in the secondary settling tank can be expressed as a nonlinear strongly degenerate PDE.
► Reliable numerical methods for simulation converge to the physically relevant solution of the PDE as the discretization is refined.
► Two such methods are compared via simulations for two scenarios.
► Pitfalls when deriving numerical methods for this type of PDE are demonstrated.
► Certain methods are ruled out as unsuitable.