Name
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. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1016/j.jcp.2018.05.046 | Journal of Computational Physics |
Keywords | Field | DocType |
UQ,Darcy–Stokes flow,Contaminant transport,MLMC,Multigrid,Uzawa smoother | Alternating direction implicit method,Discretization,Applied mathematics,Monte Carlo method,Random field,Uncertainty quantification,Mathematical analysis,Upwind scheme,Multigrid method,Mathematics,Estimator | Journal |
Volume | ISSN | Citations |
371 | 0021-9991 | 1 |
PageRank | References | Authors |
0.35 | 16 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Prashant Kumar | 1 | 8 | 4.58 |
| Peiyao Luo | 2 | 3 | 1.10 |
| Francisco José Gaspar | 3 | 18 | 4.66 |
| Cornelis W. Oosterlee | 4 | 217 | 34.41 |