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    A scalable fully implicit framework for reservoir simulation on parallel computers

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    1-s2.0-S0045782517306862-main.pdf
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    Description:
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    Type
    Article
    Authors
    Yang, Haijian
    Sun, Shuyu cc
    Li, Yiteng cc
    Yang, Chao-he cc
    KAUST Department
    Computational Transport Phenomena Lab
    Earth Science and Engineering Program
    Physical Science and Engineering (PSE) Division
    KAUST Grant Number
    BAS/1/1351-01-01
    Date
    2017-11-10
    Online Publication Date
    2017-11-10
    Print Publication Date
    2018-03
    Permanent link to this record
    http://hdl.handle.net/10754/626151
    
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    Abstract
    The modeling of multiphase fluid flow in porous medium is of interest in the field of reservoir simulation. The promising numerical methods in the literature are mostly based on the explicit or semi-implicit approach, which both have certain stability restrictions on the time step size. In this work, we introduce and study a scalable fully implicit solver for the simulation of two-phase flow in a porous medium with capillarity, gravity and compressibility, which is free from the limitations of the conventional methods. In the fully implicit framework, a mixed finite element method is applied to discretize the model equations for the spatial terms, and the implicit Backward Euler scheme with adaptive time stepping is used for the temporal integration. The resultant nonlinear system arising at each time step is solved in a monolithic way by using a Newton–Krylov type method. The corresponding linear system from the Newton iteration is large sparse, nonsymmetric and ill-conditioned, consequently posing a significant challenge to the fully implicit solver. To address this issue, the family of additive Schwarz preconditioners is taken into account to accelerate the convergence of the linear system, and thereby improves the robustness of the outer Newton method. Several test cases in one, two and three dimensions are used to validate the correctness of the scheme and examine the performance of the newly developed algorithm on parallel computers.
    Citation
    Yang H, Sun S, Li Y, Yang C (2017) A scalable fully implicit framework for reservoir simulation on parallel computers. Computer Methods in Applied Mechanics and Engineering. Available: http://dx.doi.org/10.1016/j.cma.2017.10.016.
    Sponsors
    The authors would like to express their appreciations to the anonymous reviewers for the invaluable comments that have greatly improved the quality of the manuscript. The work was supported in part by the National Natural Science Foundation of China (11571100) and the state key laboratory program of LASG (20170062). S. Sun was also supported by KAUST through the grant BAS/1/1351-01-01.
    Publisher
    Elsevier BV
    Journal
    Computer Methods in Applied Mechanics and Engineering
    DOI
    10.1016/j.cma.2017.10.016
    Additional Links
    http://www.sciencedirect.com/science/article/pii/S0045782517306862
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.cma.2017.10.016
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