Algebraic dynamic multilevel method for embedded discrete fracture model (F-ADM)

JOURNAL OF COMPUTATIONAL PHYSICS

卷:373

Article

HosseiniMehr, Mousa^1,2  Cusini, Matteo²  Vuik, Cornelis¹  Hajibeygi, Hadi² 

[1] Delft Univ Technol, Fac Elect Engn Math & Comp Sci, Dept Appl Math, Van Mourik Broekmanweg 6, NL-2628 XE Delft, Netherlands

[2] Delft Univ Technol, Dept Geosci & Engn, Fac Civil Engn & Geosci, Stevinweg 1, NL-2628 CV Delft, Netherlands

关键词: Flow in porous media;    Adaptive mesh refinement;    Multiscale basis functions;    Algebraic multiscale method;    Multilevel multiscale method;    Fractured porous media;    Scalable physics-based nonlinear simulation;   

DOI  :  10.1016/j.jcp.2018.06.075

来源: Elsevier

【 摘 要 】

We present an algebraic dynamic multilevel method for multiphase flow in heterogeneous fractured porous media (F-ADM), where fractures are resolved at fine scale with an embedded discrete modelling approach. This fine-scale discrete system employs independent fine-scale computational grids for heterogeneous matrix and discrete fractures, which results in linear system sizes out of the scope of the classical simulation approaches. To reduce the computational costs, yet provide accurate solutions, on this highly resolved fine-scale mesh, F-ADM imposes independent dynamic multilevel coarse grids for both matrix and lower-dimensional discrete fractures. The fully-implicit discrete system is then mapped into this adaptive dynamic multilevel resolution for all unknowns (i.e., pressure and phase saturation). The dynamic resolution aims for resolving sharp fronts for the transport unknowns, thus constant interpolators are used to map the saturation from coarse to fine grids both in matrix and fractures. However, due to the global nature of the pressure unknowns, local multilevel basis functions for both matrix and fractures with flexible matrix-fracture coupling treatment are introduced for the pressure. The assembly of the full sets of basis functions allows for mapping the solutions up and down between any resolutions. Due to its adaptive multilevel resolution, F-ADM develops an automatic integrated framework to homogenise or explicitly represent a fracture network at a coarser level by selection of the multilevel coarse nodes in each sub-domain. Various test cases, including multiphase flow in 2D and 3D media, are studied, where only a fraction of the fine-scale grids is employed to obtain accurate nonlinear multiphase solutions. FADM casts a promising approach for large-scale simulation of multiphase flow in fractured media. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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