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ABSTRACT
A time-dependent two-scale multiphase model for precipitation in porous media is considered, which has recently been proposed and investigated numerically. For numerical treatment, the microscale model needs to be finely resolved due to moving discontinuities modelled by several phase-field functions. This results in high computational demands due to the need of resolving many such highly resolved cell problems in course of the two-scale simulation. In this article, we present a model order reduction technique for this model, which combines different ingredients such as proper orthogonal decomposition for construction of the approximating spaces, the empirical interpolation method for parameter dependency and multiple basis sets for treating the high solution variability. The resulting reduced model experimentally demonstrates considerable acceleration and good accuracy both in reproduction as well as generalization experiments.
Acknowledgements
The authors would like to thank the Baden-Württemberg Stiftung gGmbH for funding this project. Also, we thank the German Research Foundation (DFG) for financial support within the Cluster of Excellence in Simulation Technology: [Grant Number EXC 310/1] and within the International Research Training Group ‘Nonlinearities and upscaling in porous media’ [NUPUS, IRTG 1398] at the University of Stuttgart.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1. We give a short motivation for this choice of snapshots for EI: Equation (15) is equivalent to the root finding problem . Standard training snapshots
are always zero, hence carry no suitable information. Motivated by the Newton fixpoint iteration
we realize that for good approximation of this system (and thus good approximation of the fixpoint, i.e. the root) it seems reasonable to collect snapshots
for constructing an EI space. In this sense, we are realizing an EI for the linearized root finding problem, which in our case is the original linear problem (15).