TY - JOUR
T1 - A multigrid multilevel Monte Carlo method for transport in the Darcy–Stokes system
AU - Kumar, Prashant
AU - Luo, Peiyao
AU - Gaspar, Francisco J.
AU - Oosterlee, Cornelis W.
PY - 2018/10/15
Y1 - 2018/10/15
N2 - 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.
AB - 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.
KW - Contaminant transport
KW - Darcy–Stokes flow
KW - MLMC
KW - Multigrid
KW - UQ
KW - Uzawa smoother
UR - http://www.scopus.com/inward/record.url?scp=85048527017&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2018.05.046
DO - 10.1016/j.jcp.2018.05.046
M3 - Article
AN - SCOPUS:85048527017
SN - 0021-9991
VL - 371
SP - 382
EP - 408
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -