Uncertainty Quantification for a Clarifier-Thickener Model with Random Feed

Abstract

The continuous sedimentation process in a clarifier-thickener can be described by a scalar nonlinear conservation law for the solid volume fraction. The flux is discontinuous with respect to space due to the feed mechanism. Typically the feed flux cannot be given in an exact manner. To quantify uncertainty the unknown solid concentration and the feed bulk flow are expressed by polynomial chaos. A deterministic hyperbolic system for a finite number of stochastic moments is constructed. For the resulting high-dimensional system a simple finite volume scheme is presented. Numerical experiments cover one- and two-dimensional situations. © Springer-Verlag Berlin Heidelberg 2011.