Ilja Kröker

@incollection {hyp16-bk,
author = {Andrea Barth and Ilja Kröker} ,
title = {Finite volume methods for hyperbolic partial differential equations with spatial noise} ,
publisher = {Springer International Publishing} ,
year = {2016} ,
volume = {submitted} }

@inbook {Buerger2017,
author = {Bürger, Raimund and Kröker, Ilja} ,
editor = {Cancès, Clément and Omnes, Pascal} ,
title = {Hybrid Stochastic Galerkin Finite Volumes for the Diffusively Corrected Lighthill-Whitham-Richards Traffic Model} ,
booktitle = {Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems: FVCA 8, Lille, France, June 2017} ,
publisher = {Springer International Publishing} ,
year = {2017} ,
pages = {189--197} ,
url = {http://dx.doi.org/10.1007/978-3-319-57394-6_21} ,
doi = {10.1007/978-3-319-57394-6_21} }

@techreport {UQcomparison2017,
author = {Köppel, M. and Franzelin, F. and Kröker, I. and Oladyshkin, S. and Santin, G. and Wittwar, D. and Barth, A. and Haasdonk, B. and Nowak, W. and Pflüger, D. and Rohde, C.} ,
title = {Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario} ,
year = {2017} ,
url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=1759} }

Abstract: A variety of methods is available to quantify uncertainties arising within the modeling of flow and transport in carbon dioxide storage, but there is a lack of thorough comparisons. Usually, raw data from such storage sites can hardly be described by theoretical statistical distributions since only very limited data is available. Hence, exact information on distribution shapes for all uncertain parameters is very rare in realistic applications. We discuss and compare four different methods tested for data-driven uncertainty quantification based on a benchmark scenario of carbon dioxide storage. In the benchmark, for which we provide data and code, carbon dioxide is injected into a saline aquifer modeled by the nonlinear capillarity-free fractional flow formulation for two incompressible fluid phases, namely carbon dioxide and brine. To cover different aspects of uncertainty quantification, we incorporate various sources of uncertainty such as uncertainty of boundary conditions, of conceptual model definitions and of material properties. We consider recent versions of the following non-intrusive and intrusive uncertainty quantification methods: arbitary polynomial chaos, spatially adaptive sparse grids, kernel-based greedy interpolation and hybrid stochastic Galerkin. The performance of each approach is demonstrated assessing expectation value and standard deviation of the carbon dioxide saturation against a reference statistic based on Monte Carlo sampling. We compare the convergence of all methods reporting on accuracy with respect to the number of model runs and resolution. Finally we offer suggestions about the methods’ advantages and disadvantages that can guide the modeler for uncertainty quantification in carbon dioxide storage and beyond.

@article {Koeppel2016,
author = {Köppel, Markus and Kröker, Ilja and Rohde, Christian} ,
title = {Intrusive Uncertainty Quantification for Hyperbolic-Elliptic Systems Governing Two-Phase Flow in Heterogeneous Porous Media} ,
journal = {Comput. Geosci.} ,
year = {2017} ,
volume = {21} ,
pages = {807-832} ,
url = {https://link.springer.com/article/10.1007%2Fs10596-017-9662-z} ,
doi = {10.1007/s10596-017-9662-z} }

@article {BBKR16,
author = {Barth, Andrea and Bürger, Raimund and Kröker, Ilja and Rohde, Christian} ,
title = {Computational uncertainty quantification for a clarifier-thickener model with several random perturbations: A hybrid stochastic Galerkin approach} ,
journal = {Computers & Chemical Engineering } ,
year = {2016} ,
volume = {89} ,
pages = {11 -- 26} ,
url = {http://www.sciencedirect.com/science/article/pii/S0098135416300503} ,
doi = {10.1016/j.compchemeng.2016.02.016} }

@article {knr2012,
author = {Kröker, Ilja and Nowak, Wolfgang and Rohde, Christian} ,
title = {A stochastically and spatially adaptive parallel scheme for uncertain and nonlinear two-phase flow problems} ,
journal = {Comput. Geosci.} ,
publisher = {Springer International Publishing} ,
year = {2015} ,
volume = {19} ,
number = {2} ,
pages = {269--284} ,
url = {http://dx.doi.org/10.1007/s10596-014-9464-5} ,
doi = {10.1007/s10596-014-9464-5} }

@article {Buerger2012,
author = {R. Bürger and I. Kröker and C. Rohde} ,
title = {A hybrid stochastic Galerkin method for uncertainty quantification applied to a conservation law modelling a clarifier-thickener unit} ,
journal = {ZAMM Z. Angew. Math. Mech.} ,
year = {2014} ,
volume = {94} ,
number = {10} ,
pages = {793-817} ,
url = {http://dx.doi.org/10.1002/zamm.201200174} ,
doi = {10.1002/zamm.201200174} }

@incollection {fvca7-mk,
author = {Köppel, M. and Kröker, I. and Rohde, C.} ,
editor = {Fuhrmann, Jürgen and Ohlberger, Mario and Rohde, Christian} ,
title = {Stochastic Modeling for Heterogeneous Two-Phase Flow} ,
booktitle = {Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects} ,
publisher = {Springer International Publishing} ,
year = {2014} ,
volume = {77} ,
pages = {353-361} ,
url = {http://dx.doi.org/10.1007/978-3-319-05684-5_34} ,
doi = {10.1007/978-3-319-05684-5_34} }

@phdthesis {ik_Diss,
author = {Ilja Kröker} ,
title = {Stochastic models for nonlinear convection-dominated flows } ,
school = {Universität Stuttgart} ,
year = {2013} }

@article {MR2899255,
author = {Kröker, I. and Rohde, C.} ,
title = {Finite volume schemes for hyperbolic balance laws with multiplicative noise} ,
journal = {Appl. Numer. Math.} ,
year = {2012} ,
volume = {62} ,
number = {4} ,
pages = {441--456} ,
url = {http://dx.doi.org/10.1016/j.apnum.2011.01.011} ,
doi = {10.1016/j.apnum.2011.01.011} }

@incollection {MR2815639,
author = {Bürger, Raimund and Kröker, Ilja and Rohde, Christian} ,
title = {Uncertainty quantification for a clarifier-thickener model with random feed} ,
booktitle = {Finite volumes for complex applications. VI. Problems & perspectives. Volume 1, 2} ,
publisher = {Springer} ,
year = {2011} ,
volume = {4} ,
pages = {195--203} ,
url = {http://dx.doi.org/10.1007/978-3-642-20671-9_21} ,
doi = {10.1007/978-3-642-20671-9_21} }

@incollection {MR2451449,
author = {Ilja Kröker} ,
title = {Finite volume methods for conservation laws with noise} ,
booktitle = {Finite volumes for complex applications V} ,
publisher = {ISTE, London} ,
year = {2008} ,
pages = {527--534} }