Open AccessA Galerkin‐free/equation‐free model reduction method for single‐phase flow in fractured porous media
Author(s) -
Han Dongxu,
Li Tingyu,
Tang Qingfeng,
Yu Bo,
Sun Dongliang
Publication year - 2020
Publication title -
energy science and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.638
H-Index - 29
ISSN - 2050-0505
DOI - 10.1002/ese3.643
Subject(s) - galerkin method , discontinuous galerkin method , flow (mathematics) , porous medium , point of delivery , fluid dynamics , mathematics , computer science , mathematical optimization , porosity , finite element method , mechanics , materials science , physics , geometry , structural engineering , engineering , agronomy , composite material , biology
Using traditional high‐fidelity numerical simulation to simulate fluid flow in fractured porous media in a real field remains challenging. It involves a large number of degrees of freedom when matrix and fracture equations are solved. To address this challenge, we propose a Galerkin‐free framework to construct a reduced‐order model (ROM) based on the proper orthogonal decomposition (POD). Compared with the typical POD‐based modeling process commonly used in previous studies, the POD‐ROM can be built without performing the Galerkin projection of flow equations onto the low‐dimensional space spanned by the POD basis functions. The numerical integration method was incorporated to obtain the POD time coefficients based on the flow equations solved by the conventional finite volume method. Two complex fracture cases reflecting high‐contrast porous media in a two‐dimensional domain were designed to verify the accuracy and efficiency of the established Galerkin‐free POD‐ROM. Sensitivity analysis of parameters was conducted to examine the adaptability of the ROM. The results illustrate that, compared with the fine‐scale model, the ROM can significantly reduce the CPU time without compromising the quality of the numerical solutions.