## Preprint 2016-17

## Raimund Bürger, Stefan Diehl, Camilo Mejías:

### A model of continuous sedimentation with compression and reactions

### Abstract:

Continuously operated settling tanks are used for the gravity separation of solid-liquid suspensions in several industries. Mathematical models of these units have been a topic for well-posedness and numerical analysis even in one space dimension due to the spatially discontinuous coefficients of the underlying strongly degenerate parabolic, nonlinear model PDE. Such a model is extended to describe the sedimentation of multi-component particles that undergo reactions with several soluble constituents of the liquid phase. The fundamental equations are reformulated as a system of model PDEs for which a new numerical scheme is formulated. This scheme combines a difference scheme for conservation laws with discontinuous flux with an approach of numerical percentage propagation for multi-component flows. The main result is an invariant region property, which implies that physically relevant numerical solutions are produced. Simulations of denitrification in secondary settling tanks in wastewater treatment illustrate the model and its discretization.