dc.date.accessioned | 2013-03-12T08:19:21Z | |
dc.date.available | 2013-03-12T08:19:21Z | |
dc.date.issued | 2005 | en_US |
dc.date.submitted | 2009-11-25 | en_US |
dc.identifier.uri | http://hdl.handle.net/10852/10588 | |
dc.description.abstract | A well-studied one-dimensional model for the operation of clarifier-thickener units in engineering applications can be expressed as a conservation law with a flux that is discontinuous with respect to the spatial variable. This model also includes a singular feed source. In this paper, the clarifier-thickener model is extended by a singular sink through which material is extracted from the unit. A difficulty is that in contrast to the singular source, the sink term cannot be incorporated into the flux function; rather, the sink is represented by a new non-conservative transport term. The paper is concerned with the well-posedness analysis and numerical methods for the extended model. To simplify the analysis, a reduced problem is formulated, which contains the new sink term of the extended clarifier-thickener model, but not the source term and flux discontinuities that can be handled by existing methods. A definition of entropy solutions, based on Kruzkov-type entropy functions and fluxes, is provided. Jump conditions are derived and uniqueness of the entropy solution is shown. Existence of an entropy solution is shown by proving convergence of a monotone difference scheme. Combining the present analysis for the reduced problem with previous results [Numer. Math. 97 (2004) 25-65] shows that the full extended clarifier-thickener model is well-posed. Two variants of the numerical scheme are introduced. Numerical examples illustrate that all three variants converge to the entropy solution, but introduce different amounts of numerical diffusion. | eng |
dc.language.iso | eng | en_US |
dc.publisher | Matematisk Institutt, Universitetet i Oslo | |
dc.relation.ispartof | Preprint series. Pure mathematics http://urn.nb.no/URN:NBN:no-8076 | en_US |
dc.relation.uri | http://urn.nb.no/URN:NBN:no-8076 | |
dc.rights | © The Author(s) (2005). This material is protected by copyright law. Without explicit authorisation, reproduction is only allowed in so far as it is permitted by law or by agreement with a collecting society. | |
dc.title | ON AN EXTENDED CLARIFIER-THICKENER MODEL WITH SINGULAR SOURCE AND SINK TERM | en_US |
dc.type | Research report | en_US |
dc.date.updated | 2009-11-26 | en_US |
dc.rights.holder | Copyright 2005 The Author(s) | |
dc.creator.author | Bürger, Raimund | en_US |
dc.creator.author | García, A. | en_US |
dc.creator.author | Karlsen, Kenneth H. | en_US |
dc.creator.author | Towers, John D. | en_US |
dc.subject.nsi | VDP::410 | en_US |
dc.identifier.urn | URN:NBN:no-23636 | en_US |
dc.type.document | Forskningsrapport | en_US |
dc.identifier.duo | 97332 | en_US |
dc.identifier.fulltext | Fulltext https://www.duo.uio.no/bitstream/handle/10852/10588/1/pm33-05.pdf | |