%0 Journal Article %1 ISI:000376202800002 %A Barth, Andrea %A Burger, Raimund %A Kroeker, Ilja %A Rohde, Christian %C THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND %D 2016 %I PERGAMON-ELSEVIER SCIENCE LTD %J COMPUTERS & CHEMICAL ENGINEERING %K Finite Galerkin Galerkin; Hybrid Polynomial Uncertainty chaos; method} model; projection; quantification; stochastic volume {Clarifier-thickener %P 11-26 %R 10.1016/j.compchemeng.2016.02.016 %T Computational uncertainty quantification for a clarifier-thickener model with several random perturbations: A hybrid stochastic Galerkin approach %V 89 %X Continuous sedimentation processes in a clarifier-thickener unit can be described by a scalar nonlinear conservation law whose flux density function is discontinuous with respect to the spatial position. In the applications of this model, which include mineral processing and wastewater treatment, the rate and composition of the feed flow cannot be given deterministically. Efficient numerical simulation is required to quantify the effect of uncertainty in these control parameters in terms of the response of the clarifier thickener system. Thus, the problem at hand is one of uncertainty quantification for nonlinear hyperbolic problems with several random perturbations. The presented hybrid stochastic Galerkin method is devised so as to extend the polynomial chaos approximation by multiresolution discretization in the stochastic space. This approach leads to a deterministic hyperbolic system, which is partially decoupled and therefore suitable for efficient parallelisation. Stochastic adaptivity reduces the computational effort. Several numerical experiments are presented. (C) 2016 Elsevier Ltd. All rights reserved.

@article{ISI:000376202800002, abstract = {{Continuous sedimentation processes in a clarifier-thickener unit can be described by a scalar nonlinear conservation law whose flux density function is discontinuous with respect to the spatial position. In the applications of this model, which include mineral processing and wastewater treatment, the rate and composition of the feed flow cannot be given deterministically. Efficient numerical simulation is required to quantify the effect of uncertainty in these control parameters in terms of the response of the clarifier thickener system. Thus, the problem at hand is one of uncertainty quantification for nonlinear hyperbolic problems with several random perturbations. The presented hybrid stochastic Galerkin method is devised so as to extend the polynomial chaos approximation by multiresolution discretization in the stochastic space. This approach leads to a deterministic hyperbolic system, which is partially decoupled and therefore suitable for efficient parallelisation. Stochastic adaptivity reduces the computational effort. Several numerical experiments are presented. (C) 2016 Elsevier Ltd. All rights reserved.}}, added-at = {2017-05-18T11:32:12.000+0200}, address = {{THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND}}, affiliation = {{Kroker, I (Reprint Author), Univ Stuttgart, IANS, Pfaffenwaldring 57, D-70569 Stuttgart, Germany. Burger, Raimund, Univ Concepcion, CI2MA, Casilla 160-C, Concepcion, Chile. Burger, Raimund, Univ Concepcion, Dipartimento Ingn Matemat, Casilla 160-C, Concepcion, Chile. Barth, Andrea; Kroeker, Ilja; Rohde, Christian, Univ Stuttgart, IANS, Pfaffenwaldring 57, D-70569 Stuttgart, Germany.}}, author = {Barth, Andrea and Burger, Raimund and Kroeker, Ilja and Rohde, Christian}, author-email = {{ikroeker@mathematik.uni-stuttgart.de}}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2cffcf9b4d25fbc122de56edd6f23f805/hermann}, doi = {{10.1016/j.compchemeng.2016.02.016}}, eissn = {{1873-4375}}, funding-acknowledgement = {{German Research Foundation (DFG) within the Cluster of Excellence in Simulation Technology at the University of Stuttgart {[}EXC 310/1]; Fondecyt project {[}1130154]; Fondef project {[}1D15I10291]; Conicyt project Anillo {[}ACT1118]; MINE-DUC project at Universidad de Concepcion {[}UCO1202]; BASAL project CMM; Universidad de Chile; Centro de Investigacion en Ingenieria Matematica (CI<SUP>2</SUP>MA); Universidad de Concepcion; Centro CRHIAM Proyecto Conicyt Fondap {[}15130015]; Red Doctoral REDOC.CTA}}, funding-text = {{A.B., 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. R.B. is supported by Fondecyt project 1130154; Fondef project 1D15I10291; Conicyt project Anillo ACT1118 (ANANUM); Red Doctoral REDOC.CTA, MINE-DUC project UCO1202 at Universidad de Concepcion; BASAL project CMM, Universidad de Chile and Centro de Investigacion en Ingenieria Matematica (CI<SUP>2</SUP>MA), Universidad de Concepcion; and Centro CRHIAM Proyecto Conicyt Fondap 15130015.}}, interhash = {158d6d69825141720526007acae4fa2b}, intrahash = {cffcf9b4d25fbc122de56edd6f23f805}, issn = {{0098-1354}}, journal = {{COMPUTERS \& CHEMICAL ENGINEERING}}, keywords = {Finite Galerkin Galerkin; Hybrid Polynomial Uncertainty chaos; method} model; projection; quantification; stochastic volume {Clarifier-thickener}, keywords-plus = {{SECONDARY SETTLING TANKS; HYPERBOLIC CONSERVATION-LAWS; DISCONTINUOUS FLUX FUNCTION; CONTINUOUS SEDIMENTATION; OPERATING CHARTS; NUMERICAL-METHODS; FLOW PROBLEMS; SIMULATION; SCHEMES; SUSPENSIONS}}, language = {{English}}, month = {{JUN 9}}, number-of-cited-references = {{52}}, pages = {{11-26}}, publisher = {{PERGAMON-ELSEVIER SCIENCE LTD}}, research-areas = {{Computer Science; Engineering}}, times-cited = {{0}}, timestamp = {2017-05-18T09:32:12.000+0200}, title = {{Computational uncertainty quantification for a clarifier-thickener model with several random perturbations: A hybrid stochastic Galerkin approach}}, type = {{Article}}, volume = {{89}}, web-of-science-categories = {{Computer Science, Interdisciplinary Applications; Engineering, Chemical}}, year = {{2016}} }