C-AMS

Adaptive algebraic multiscale solver for compressible flow in heterogeneous porous media. 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 [the second author et al., ibid. 259, Part A, 284--303 (2014; Zbl 06660071)], 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.


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  1. Cusini, Matteo; Fryer, Barnaby; van Kruijsdijk, Cor; Hajibeygi, Hadi: Algebraic dynamic multilevel method for compositional flow in heterogeneous porous media (2018)
  2. Praditia, Timothy; Helmig, Rainer; Hajibeygi, Hadi: Multiscale formulation for coupled flow-heat equations arising from single-phase flow in fractured geothermal reservoirs (2018)
  3. Bosma, Sebastian; Hajibeygi, Hadi; Tene, Matei; Tchelepi, Hamdi A.: Multiscale finite volume method for discrete fracture modeling on unstructured grids (MS-DFM) (2017)
  4. Cortinovis, Davide; Jenny, Patrick: Zonal multiscale finite-volume framework (2017)
  5. de Moraes, Rafael J.; Rodrigues, José R. P.; Hajibeygi, Hadi; Jansen, Jan Dirk: Multiscale gradient computation for flow in heterogeneous porous media (2017)
  6. Scovazzi, Guglielmo; Wheeler, Mary F.; Mikelić, Andro; Lee, Sanghyun: Analytical and variational numerical methods for unstable miscible displacement flows in porous media (2017)
  7. Cusini, Matteo; van Kruijsdijk, Cor; Hajibeygi, Hadi: Algebraic dynamic multilevel (ADM) method for fully implicit simulations of multiphase flow in porous media (2016)
  8. Shah, Swej; Møyner, Olav; Tene, Matei; Lie, Knut-Andreas; Hajibeygi, Hadi: The multiscale restriction smoothed basis method for fractured porous media (F-MSRSB) (2016)
  9. Ţene, Matei; Al Kobaisi, Mohammed Saad; Hajibeygi, Hadi: Algebraic multiscale method for flow in heterogeneous porous media with embedded discrete fractures (F-AMS) (2016)
  10. Ţene, Matei; Wang, Yixuan; Hajibeygi, Hadi: Adaptive algebraic multiscale solver for compressible flow in heterogeneous porous media (2015)