Stochastic multiscale flux basis for Stokes-Darcy flows

Ambartsumyan, Ilona; Khattatov, Eldar; Wang, ChangQing; Yotov, Ivan

doi:10.1016/j.jcp.2019.109011

Stochastic multiscale flux basis for Stokes-Darcy flows

Journal Article · Thu Oct 17 00:00:00 EDT 2019 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2019.109011· OSTI ID:1800166

Ambartsumyan, Ilona ^[1]; Khattatov, Eldar ^[2]; Wang, ChangQing ^[2]; ^[2]

Univ. of Pittsburgh, PA (United States); OSTI
Univ. of Pittsburgh, PA (United States)

Three algorithms are developed for uncertainty quantification in modeling coupled Stokes and Darcy flows. The porous media may consist of multiple regions with different properties. The permeability is modeled as a non-stationary stochastic variable, with its log represented as a sum of local Karhunen-Loève (KL) expansions. The problem is approximated by stochastic collocation on either tensor-product or sparse grids, coupled with a multiscale mortar mixed finite element method for the spatial discretization. A non-overlapping domain decomposition algorithm reduces the global problem to a coarse scale mortar interface problem, which is solved by an iterative solver, for each stochastic realization. In the traditional domain decomposition implementation, each subdomain solves a local Dirichlet or Neumann problem in every interface iteration. To reduce this cost, two additional algorithms based on deterministic or stochastic multiscale flux basis are introduced. The basis consists of the local flux (or velocity trace) responses from each mortar degree of freedom. It is computed for each subdomain independently before the interface iteration begins. The use of the multiscale flux basis avoids the need for subdomain solves on each iteration. The deterministic basis is computed at each stochastic collocation and used only at this realization. The stochastic basis is formed by further looping over all local realizations of a subdomain's KL region before the stochastic collocation begins. It is used over multiple realizations. Numerical tests are presented to illustrate the performance of the three algorithms, with the stochastic multiscale flux basis showing significant savings in computational cost compared to the other two algorithms.

View Accepted Manuscript (DOE)

Research Organization:: University of Pittsburgh, PA (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC)

Grant/Contract Number:: FG02-04ER25618

OSTI ID:: 1800166

Alternate ID(s):: OSTI ID: 1576809

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 401; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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