A multigrid multilevel Monte Carlo method for transport in the Darcy–Stokes system

Title

A multigrid multilevel Monte Carlo method for transport in the Darcy–Stokes system

 Author

Kumar, P. (TU Delft Aerodynamics; Centrum Wiskunde & Informatica (CWI))
Luo, P. (TU Delft Numerical Analysis)
Gaspar, Francisco J. (Centrum Wiskunde & Informatica (CWI))
Oosterlee, C.W. (TU Delft Numerical Analysis; Centrum Wiskunde & Informatica (CWI)) ORCID 0000-0002-7322-4094

 Date

2018-10-15

 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.


 Subject

Contaminant transport
Darcy–Stokes flow
MLMC
Multigrid
UQ
Uzawa smoother

 To reference this document use:

http://resolver.tudelft.nl/uuid:c51c3c70-f834-4867-bc0f-22677e896402

 DOI

https://doi.org/10.1016/j.jcp.2018.05.046

 Embargo date

2020-06-14

 ISSN

0021-9991

 Source

Journal of Computational Physics, 371, 382-408

 Part of collection

Institutional Repository

 Document type

journal article

 Rights

© 2018 P. Kumar, P. Luo, Francisco J. Gaspar, C.W. Oosterlee
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