Proper orthogonal decomposition reduced model for mass transport in heterogenous media |
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| Authors: | Xinya Li Bill X Hu |
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| Institution: | 1. Hydrology, Energy and Environment Directorate, Pacific Northwest National Laboratory, Richland, WA, 99352, USA
2. Department of Earth, Ocean and Atmospheric Science, Florida State University, Tallahassee, FL, 32306, USA
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| Abstract: | Numerical models with fine discretization normally demand large computational time and space, which lead to computational burden for state estimations or model parameter inversion calculation. This article presented a reduced implicit finite difference scheme that based on proper orthogonal decomposition (POD) for two-dimensional transient mass transport in heterogeneous media. The reduction of the original full model was achieved by projecting the high-dimension full model to a low-dimension space created by POD bases, and the bases are derived from the snapshots generated from the model solutions of the forward simulations. The POD bases were extracted from the ensemble of snapshots by singular value decomposition. The dimension of the Jacobian matrix was then reduced after Galerkin projection. Thus, the reduced model can accurately reproduce and predict the original model’s transport process with significantly decreased computational time. This scheme is practicable with easy implementation of the partial differential equations. The POD method is illustrated and validated through synthetic cases with various heterogeneous permeability field scenarios. The accuracy and efficiency of the reduced model are determined by the optimal selection of the snapshots and POD bases. |
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