02 Fakultät Bau- und Umweltingenieurwissenschaften

Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/3

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Institute: search.filters.UBSInstitut.Institut für Angewandte Analysis und numerische SimulationAuthor: search.filters.author.Oladyshkin, Sergey

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    A surrogate-assisted uncertainty-aware Bayesian validation framework and its application to coupling free flow and porous-medium flow
    (2023) Mohammadi, Farid; Eggenweiler, Elissa; Flemisch, Bernd; Oladyshkin, Sergey; Rybak, Iryna; Schneider, Martin; Weishaupt, Kilian
    Existing model validation studies in geoscience often disregard or partly account for uncertainties in observations, model choices, and input parameters. In this work, we develop a statistical framework that incorporates a probabilistic modeling technique using a fully Bayesian approach to perform a quantitative uncertainty-aware validation. A Bayesian perspective on a validation task yields an optimal bias-variance trade-off against the reference data. It provides an integrative metric for model validation that incorporates parameter and conceptual uncertainty. Additionally, a surrogate modeling technique, namely Bayesian Sparse Polynomial Chaos Expansion, is employed to accelerate the computationally demanding Bayesian calibration and validation. We apply this validation framework to perform a comparative evaluation of models for coupling a free flow with a porous-medium flow. The correct choice of interface conditions and proper model parameters for such coupled flow systems is crucial for physically consistent modeling and accurate numerical simulations of applications. We develop a benchmark scenario that uses the Stokes equations to describe the free flow and considers different models for the porous-medium compartment and the coupling at the fluid-porous interface. These models include a porous-medium model using Darcy’s law at the representative elementary volume scale with classical or generalized interface conditions and a pore-network model with its related coupling approach. We study the coupled flow problems’ behaviors considering a benchmark case, where a pore-scale resolved model provides the reference solution. With the suggested framework, we perform sensitivity analysis, quantify the parametric uncertainties, demonstrate each model’s predictive capabilities, and make a probabilistic model comparison.
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    Global sensitivity analysis using multi-resolution polynomial chaos expansion for coupled Stokes-Darcy flow problems
    (2023) Kröker, Ilja; Oladyshkin, Sergey; Rybak, Iryna
    Determination of relevant model parameters is crucial for accurate mathematical modelling and efficient numerical simulation of a wide spectrum of applications in geosciences. The conventional method of choice is the global sensitivity analysis (GSA). Unfortunately, at least the classical Monte-Carlo based GSA requires a high number of model runs. Response surfaces based techniques, e.g. arbitrary Polynomial Chaos (aPC) expansion, can reduce computational effort, however, they suffer from the Gibbs phenomena and high hardware requirements for higher accuracy. We introduce GSA for arbitrary Multi-Resolution Polynomial Chaos (aMR-PC) which is a localized aPC based data-driven polynomial discretization. The aMR-PC allows to reduce the Gibbs phenomena by construction and to achieve higher accuracy by means of localization also for lower polynomial degrees. We apply these techniques to perform the sensitivity analysis for the Stokes-Darcy problem which describes fluid flow in coupled free-flow and porous-medium systems. We consider the Stokes equations in the free-flow region, Darcy’s law in the porous-medium domain and the classical interface conditions across the fluid–porous interface including the conservation of mass, the balance of normal forces and the Beavers–Joseph condition for the tangential velocity. This coupled problem formulation contains four uncertain parameters: the exact location of the interface, the permeability, the Beavers-Joseph slip coefficient and the uncertainty in the boundary conditions. We carry out the sensitivity analysis of the coupled model with respect to these parameters using the Sobol indices on the aMR-PC expansion and conduct the corresponding numerical simulations.