Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6928666 | Journal of Computational Physics | 2018 | 35 Pages |
Abstract
A multilevel Monte Carlo (MLMC) method for Uncertainty Quantification (UQ) of advection-dominated contaminant transport in a coupled Darcy-Stokes flow system is described. In particular, we focus on high-dimensional epistemic uncertainty due to an unknown permeability field in the Darcy domain that is modelled as a lognormal random field. This paper explores different numerical strategies for the subproblems and suggests an optimal combination for the MLMC estimator. We propose a specific monolithic multigrid algorithm to efficiently solve the steady-state Darcy-Stokes flow with a highly heterogeneous diffusion coefficient. Furthermore, we describe an Alternating Direction Implicit (ADI) based time-stepping for the flux-limited quadratic upwinding discretization for the transport problem. Numerical experiments illustrating the multigrid convergence and cost of the MLMC estimator with respect to the smoothness of permeability field are presented.
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Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
Prashant Kumar, Peiyao Luo, Francisco J. Gaspar, Cornelis W. Oosterlee,