Numerical simulation of clarifier-thickener units treating ideal suspensions with a flux density function having two inflection points

Abstract

We consider a nonconvex conservation law modelling the settling of particles in ideal clarifier-thickener units. The flux function of this conservation law has an explicit spatial dependence that is discontinuous. Previous works by two of the authors, together with collaborators, have been aimed at providing a firm rigorous ground of mathematical (global existence and uniqueness) and numerical analysis for clarifier-thickener models. Although the results of these works are briefly summarized herein, the chief goal of this paper is to present a number of numerical simulations of practical interest and to draw some conclusions from them. In contrast to previous papers we consider here flux density functions with two inflection points, which result in solutions exhibiting a richer structure than for flux density functions having one inflection point. The relevance of the “two inflection point” case comes from experimental observations. In addition, we include here several numerical simulations in which the feed rate and overflow and underflow bulk rates vary with time. Time dependent situations have high practical value, but have been very little studied in the literature.