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The Multiscale Robin Coupled Method for flows in porous media

Guiraldello, Rafael T. ; Ausas, Roberto F. ; Sousa, Fabricio S. ; Pereira, Felipe ; Buscaglia, Gustavo C.

Journal of computational physics, 2018-02, Vol.355, p.1-21 [Periódico revisado por pares]

Cambridge: Elsevier Inc

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  • Título:
    The Multiscale Robin Coupled Method for flows in porous media
  • Autor: Guiraldello, Rafael T. ; Ausas, Roberto F. ; Sousa, Fabricio S. ; Pereira, Felipe ; Buscaglia, Gustavo C.
  • Assuntos: Boundary conditions ; Computer simulation ; Darcy flow ; Decomposition ; Domain decomposition ; Domain decomposition methods ; Finite element method ; Fluxes ; Mortars (material) ; Multiscale analysis ; Multiscale approximation ; Optimized Schwarz ; Parameters ; Permeability ; Porosity ; Porous media ; Robin boundary conditions ; Studies ; Two-Lagrange-multiplier method ; Velocity ; Velocity distribution ; Well posed problems
  • É parte de: Journal of computational physics, 2018-02, Vol.355, p.1-21
  • Descrição: A multiscale mixed method aiming at the accurate approximation of velocity and pressure fields in heterogeneous porous media is proposed. The procedure is based on a new domain decomposition method in which the local problems are subject to Robin boundary conditions. The domain decomposition procedure is defined in terms of two independent spaces on the skeleton of the decomposition, corresponding to interface pressures and fluxes, that can be chosen with great flexibility to accommodate local features of the underlying permeability fields. The well-posedness of the new domain decomposition procedure is established and its connection with the method of Douglas et al. (1993) [12], is identified, also allowing us to reinterpret the known procedure as an optimized Schwarz (or Two-Lagrange-Multiplier) method. The multiscale property of the new domain decomposition method is indicated, and its relation with the Multiscale Mortar Mixed Finite Element Method (MMMFEM) and the Multiscale Hybrid-Mixed (MHM) Finite Element Method is discussed. Numerical simulations are presented aiming at illustrating several features of the new method. Initially we illustrate the possibility of switching from MMMFEM to MHM by suitably varying the Robin condition parameter in the new multiscale method. Then we turn our attention to realistic flows in high-contrast, channelized porous formations. We show that for a range of values of the Robin condition parameter our method provides better approximations for pressure and velocity than those computed with either the MMMFEM and the MHM. This is an indication that our method has the potential to produce more accurate velocity fields in the presence of rough, realistic permeability fields of petroleum reservoirs. •New domain decomposition method based on Robin conditions for Darcy flow is proposed.•Design and implementation of an associated multiscale method is given.•Relation of the new procedure with well known existing methods is established.•Careful comparison of results with two well known multiscale methods.•Evidence of improved accuracy for realistic highly variable permeability fields.
  • Editor: Cambridge: Elsevier Inc
  • Idioma: Inglês
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  • Realização: ABCD-USP USP   Logos de Redes Sociais: Freepik

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