Thesis defence P. Kumar: flows

16 July 2019 10:00 - Location: Aula, TU Delft - By: webredactie

Multilevel Solvers for Stochastic Fluid Flows. Promotor 1: Dr. R.P. Dwight (LR); Promotor 2: Prof.dr.ir. C.W. Oosterlee (EWI).

Uncertainty is ubiquitous in many areas of science and engineering. It may result from the inadequacy of mathematical models to represent the reality or from unknown physical parameters that are required as inputs for these models. Uncertainty may also arise due to the inherent randomness of the system being analyzed. For many problems of practical interest, uncertainty quantification can involve computations that are intractable even for the modern supercomputers, if conventional mathematical techniques are utilized. The reason is typically a product of complexity factors associated with many samples needed to compute the statistics, and for each sample, complexity associated with the spatio-temporal scales characteristics to the system.

The PhD research is focused on the development of multilevel solvers for stochastic fluid flow problems with high-dimensional uncertainties. The complexity arising due to sampling is overcome by the multilevel Monte Carlo method and complexity due to spatio-temporal scales is eliminated via the multigrid solver. The  thesis reports fast and robust solvers for four classes of flow problems: single-phase flow in porous media with highly heterogeneous diffusion coefficients; a multi-physics problem involving advection-dominated transport in a coupled Darcy-Stokes system; a nonlinear multi-phase flow in variably saturated porous media; and turbulent flows with high Reynolds number. For all these problems, extremely high-dimensional uncertainties are encountered where the unknown physical parameters are modeled as an infinite-dimensional random field or even as an infinite-dimensional random tensor field.

More information?

For access to theses by the PhD students you can have a look in TU Delft Repository, the digital storage of publications of TU Delft. Theses will be available within a few weeks after the actual thesis defence.