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.
MSC2010: 65M08, 68U20, 35R60
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Acknowledgements
R. B. acknowledges support by Fondecyt project 1090456, BASAL project CMM, Universidad de Chile and Centro de Investigación en Ingeniería Matemática (CI2MA), Universidad de Concepción. I. K. and C. R. would like to thank the German Research Foundation (DFG) for financial support of the project within the Cluster of Excellence in Simulation Technology (EXC 310/1) at the University of Stuttgart.
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Bürger, R., Kröker, I., Rohde, C. (2011). Uncertainty Quantification for a Clarifier–Thickener Model with Random Feed. In: Fořt, J., Fürst, J., Halama, J., Herbin, R., Hubert, F. (eds) Finite Volumes for Complex Applications VI Problems & Perspectives. Springer Proceedings in Mathematics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20671-9_21
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DOI: https://doi.org/10.1007/978-3-642-20671-9_21
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