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    Solving global problem by considering multitude of local problems: Application to fluid flow in anisotropic porous media using the multipoint flux approximation

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    Type
    Article
    Authors
    Salama, Amgad cc
    Sun, Shuyu cc
    Wheeler, Mary Fanett
    KAUST Department
    Computational Transport Phenomena Lab
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Earth Science and Engineering Program
    Environmental Science and Engineering Program
    Physical Science and Engineering (PSE) Division
    Date
    2014-09
    Permanent link to this record
    http://hdl.handle.net/10754/563721
    
    Metadata
    Show full item record
    Abstract
    In this work we apply the experimenting pressure field approach to the numerical solution of the single phase flow problem in anisotropic porous media using the multipoint flux approximation. We apply this method to the problem of flow in saturated anisotropic porous media. In anisotropic media the component flux representation requires, generally multiple pressure values in neighboring cells (e.g., six pressure values of the neighboring cells is required in two-dimensional rectangular meshes). This apparently results in the need for a nine points stencil for the discretized pressure equation (27 points stencil in three-dimensional rectangular mesh). The coefficients associated with the discretized pressure equation are complex and require longer expressions which make their implementation prone to errors. In the experimenting pressure field technique, the matrix of coefficients is generated automatically within the solver. A set of predefined pressure fields is operated on the domain through which the velocity field is obtained. Apparently such velocity fields do not satisfy the mass conservation equations entailed by the source/sink term and boundary conditions from which the residual is calculated. In this method the experimenting pressure fields are designed such that the residual reduces to the coefficients of the pressure equation matrix. © 2014 Elsevier B.V. All rights reserved.
    Citation
    Salama, A., Sun, S., & Wheeler, M. F. (2014). Solving global problem by considering multitude of local problems: Application to fluid flow in anisotropic porous media using the multipoint flux approximation. Journal of Computational and Applied Mathematics, 267, 117–130. doi:10.1016/j.cam.2014.01.016
    Publisher
    Elsevier BV
    Journal
    Journal of Computational and Applied Mathematics
    DOI
    10.1016/j.cam.2014.01.016
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.cam.2014.01.016
    Scopus Count
    Collections
    Articles; Environmental Science and Engineering Program; Physical Science and Engineering (PSE) Division; Earth Science and Engineering Program; Computational Transport Phenomena Lab; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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