Mathematics
Surrogate modeling for uncertainty quantification in non-Newtonian fluid flows
Mathematisches Kolloquium im Wintersemester 2024/25
When?
December 18, 2024, 17:15-19:00
Where?
Hörsaal der Kernphysik
S2|14 24
Schlossgartenstr. 9
64289 Darmstadt
Organiser
FB Mathematik
Contact
Prof. Mohammed Seaid, Durham University, UK
Numerical solutions of non-Newtonian fluids using CFD tools are often influenced by uncertainties generated by a lack of knowledge of the input values related to constitutive laws for the shear rate and viscosity relation, the domain data and/or boundary conditions in the mathematical equations used in the modeling. Conventional methods for uncertainty quantification in modeling non-Newtonian fluids constitute severe challenges due to the high computational costs especially at high Reynolds numbers. For a given accuracy and a high Reynolds number it is necessary to perform a mesh convergence study by refining the discretization of the computational domain with an increased resolution, which leads to increasing the number of degrees of freedom at a much higher rate than the Reynolds numbers. To estimate the uncertainties, many model evaluations are required, but only a single surrogate model is created in the process. In the present work, we propose the use of a non-intrusive spectral projection applied to a finite element framework with enriched basis functions for the uncertainty quantification of non-Newtonian fluid flows. The method integrates (i) the mixed finite element method for the space discretization is combined with a viscosity-splitting scheme for the time integration for effectively computing the solutions of non-Newtonian fluid flows; and (ii) a non-intrusive spectral projection for effectively propagating random constitutive laws that encode uncertainties in the non-Newtonian flow problems. Compared to the conventional finite element methods, the proposed method is demonstrated to reduce the total cost of accurately computing uncertainties in non-Newtonian fluid flows with both shear-thinning and shear-thickening regimes. Numerical results are presented for several numerical tests including a problem of phosphate slurry flow with uncertainties in rheology modelling. Comparisons to the Monte Carlo simulations and the regression based polynomial chaos expansion confirm the computational effectiveness of the proposed approach.
Tags
Mathematisches Kolloquium, Mathematik, Numerik