Abstract
In this article, we develop a reduced basis method for efficiently solving the coupled Stokes/Darcy equations with parametric internal geometry. To accommodate possible changes in topology, we define the Stokes and Darcy domains implicitly via a phase-field indicator function. In our reduced order model, we approximate the parameter-dependent phase-field function with a discrete empirical interpolation method (DEIM) that enables affine decomposition of the associated linear and bilinear forms. In addition, we introduce a modification of DEIM that leads to non-negativity preserving approximations, thus guaranteeing positive-semidefiniteness of the system matrix. We also present a strategy for determining the required number of DEIM modes for a given number of reduced basis functions. We couple reduced basis functions on neighboring patches to enable the efficient simulation of large-scale problems that consist of repetitive subdomains. We apply our reduced basis framework to efficiently solve the inverse problem of characterizing the subsurface damage state of a complete in-situ leach mining site.
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Open Access funding enabled and organized by Projekt DEAL. The results presented in this paper were achieved as part of the ERC Starting Grant project “ImageToSim” that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. 759001). The authors gratefully acknowledge this support.
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Stoter, S.K., Jessen, E., Niedens, V. et al. A DEIM driven reduced basis method for the diffuse Stokes/Darcy model coupled at parametric phase-field interfaces. Comput Geosci 26, 1465–1502 (2022). https://doi.org/10.1007/s10596-022-10164-4
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DOI: https://doi.org/10.1007/s10596-022-10164-4