Multiscale model reduction for fluid infiltration simulation through dual-continuum porous media with localized uncertainties

Here, we present some Reduced Basis (RB) methods for fluid infiltration problems through certain porous media modeled as dual-continuum with localized uncertainties. We apply dimension reduction techniques to construct a reduced order model. In the RB methods, to perform the offline-online computation decomposition, the model inputs need to be affinely dependent on the uncertainties. We develop a Proper Orthogonal Decomposition and Greedy (POD-Greedy) RB method for stochastic dual-continuum models. In the POD-Greedy RB framework, for heterogeneous porous media, we need to solve the stochastic dual-continuum models many times using very fine grid to construct a set of snapshots for building optimal reduced basis. This offline computation may be very expensive. To improve the offline computational efficiency, we further develop a local-global RB method, which integrates the coupled multiscale and multicontinuum approach using Generalized Multiscale Finite Element Method (GMsFEM) to the POD-Greedy RB method. To illustrate the efficiency of the proposed methods, we present two numerical examples for stochastic dual-continuum models. Our numerical results show that both the POD-Greedy RB method and the local-global RB method greatly improve the computation efficiency with high approximation accuracy.