Adaptive algebraic multiscale solver for compressible flow in heterogeneous porous media

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• 作者：Matei 泞ene^a ; ^{m.tene@tudelft.nl" class="auth_mail" title="E-mail the corresponding author} ; Yixuan Wang^b ; ^{yixuanw@stanford.edu" class="auth_mail" title="E-mail the corresponding author} ; Hadi Hajibeygi^a ; ^{h.hajibeygi@tudelft.nl" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Multiscale methods ; Compressible flows ; Heterogeneous porous media ; Scalable linear solvers ; Multiscale finite volume method ; Multiscale finite element method ; Iterative multiscale methods ; Algebraic multiscale methods
• 刊名：Journal of Computational Physics
• 出版年：2015
• 出版时间：1 November 2015
• 年：2015
• 卷：300
• 期：Complete
• 页码：679-694
• 全文大小：2084 K

文摘

This paper presents the development of an Adaptive Algebraic Multiscale Solver for Compressible flow (C-AMS) in heterogeneous porous media. Similar to the recently developed AMS for incompressible (linear) flows (Wang et al., 2014) [19], C-AMS operates by defining primal and dual-coarse blocks on top of the fine-scale grid. These coarse grids facilitate the construction of a conservative (finite volume) coarse-scale system and the computation of local basis functions, respectively. However, unlike the incompressible (elliptic) case, the choice of equations to solve for basis functions in compressible problems is not trivial. Therefore, several basis function formulations (incompressible and compressible, with and without accumulation) are considered in order to construct an efficient multiscale prolongation operator. As for the restriction operator, C-AMS allows for both multiscale finite volume (MSFV) and finite element (MSFE) methods. Finally, in order to resolve high-frequency errors, fine-scale (pre- and post-) smoother stages are employed. In order to reduce computational expense, the C-AMS operators (prolongation, restriction, and smoothers) are updated adaptively. In addition to this, the linear system in the Newton–Raphson loop is infrequently updated. Systematic numerical experiments are performed to determine the effect of the various options, outlined above, on the C-AMS convergence behaviour. An efficient C-AMS strategy for heterogeneous 3D compressible problems is developed based on overall CPU times. Finally, C-AMS is compared against an industrial-grade Algebraic MultiGrid (AMG) solver. Results of this comparison illustrate that the C-AMS is quite efficient as a nonlinear solver, even when iterated to machine accuracy.