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Title: High resolution viscous fingering simulation in miscible displacement using a p-adaptive discontinuous Galerkin method with algebraic multigrid preconditioner

Abstract

High resolution simulation of viscous fingering can offer an accurate and detailed prediction for subsurface engineering processes involving fingering phenomena. The fully implicit discontinuous Galerkin (DG) method has been shown to be an accurate and stable method to model viscous fingering with high Peclet number and mobility ratio. In this study, we present two techniques to speedup large scale simulations of this kind. The first technique relies on a simple p-adaptive scheme in which high order basis functions are employed only in elements near the finger fronts where the concentration has a sharp change. As a result, the number of degrees of freedom is significantly reduced and the simulation yields almost identical results to the more expensive simulation with uniform high order elements throughout the mesh. The second technique for speedup involves improving the solver efficiency. We present an algebraic multigrid (AMG) preconditioner which allows the DG matrix to leverage the robust AMG preconditioner designed for the continuous Galerkin (CG) finite element method. The resulting preconditioner works effectively for fixed order DG as well as p-adaptive DG problems. Finally, with the improvements provided by the p-adaptivity and AMG preconditioning, we can perform high resolution three-dimensional viscous fingering simulations required formore » miscible displacement with high Peclet number and mobility ratio in greater detail than before for well injection problems.« less

Authors:
 [1];  [2];  [2];  [1];  [1];  [3];  [1];  [1]
  1. ExxonMobil Upstream Research Company, Spring, TX (United States)
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Numerical Analysis and Applications Dept.
  3. ExxonMobil Research and Engineering, Annandale, NJ (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); ExxonMobil Upstream Research Company, Spring, TX (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1473935
Report Number(s):
SAND-2018-9819J
Journal ID: ISSN 0021-9991; 667674
Grant/Contract Number:  
NA0003525
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 374; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; discontinuous Galerkin; viscous fingering; porous media flows; adaptive; algebraic multigrid preconditioner

Citation Formats

Becker, G., Siefert, C. M., Tuminaro, R. S., Sun, H., Valiveti, D. M., Mohan, A., Yin, J., and Huang, H. High resolution viscous fingering simulation in miscible displacement using a p-adaptive discontinuous Galerkin method with algebraic multigrid preconditioner. United States: N. p., 2018. Web. doi:10.1016/j.jcp.2018.07.003.
Becker, G., Siefert, C. M., Tuminaro, R. S., Sun, H., Valiveti, D. M., Mohan, A., Yin, J., & Huang, H. High resolution viscous fingering simulation in miscible displacement using a p-adaptive discontinuous Galerkin method with algebraic multigrid preconditioner. United States. doi:10.1016/j.jcp.2018.07.003.
Becker, G., Siefert, C. M., Tuminaro, R. S., Sun, H., Valiveti, D. M., Mohan, A., Yin, J., and Huang, H. Mon . "High resolution viscous fingering simulation in miscible displacement using a p-adaptive discontinuous Galerkin method with algebraic multigrid preconditioner". United States. doi:10.1016/j.jcp.2018.07.003. https://www.osti.gov/servlets/purl/1473935.
@article{osti_1473935,
title = {High resolution viscous fingering simulation in miscible displacement using a p-adaptive discontinuous Galerkin method with algebraic multigrid preconditioner},
author = {Becker, G. and Siefert, C. M. and Tuminaro, R. S. and Sun, H. and Valiveti, D. M. and Mohan, A. and Yin, J. and Huang, H.},
abstractNote = {High resolution simulation of viscous fingering can offer an accurate and detailed prediction for subsurface engineering processes involving fingering phenomena. The fully implicit discontinuous Galerkin (DG) method has been shown to be an accurate and stable method to model viscous fingering with high Peclet number and mobility ratio. In this study, we present two techniques to speedup large scale simulations of this kind. The first technique relies on a simple p-adaptive scheme in which high order basis functions are employed only in elements near the finger fronts where the concentration has a sharp change. As a result, the number of degrees of freedom is significantly reduced and the simulation yields almost identical results to the more expensive simulation with uniform high order elements throughout the mesh. The second technique for speedup involves improving the solver efficiency. We present an algebraic multigrid (AMG) preconditioner which allows the DG matrix to leverage the robust AMG preconditioner designed for the continuous Galerkin (CG) finite element method. The resulting preconditioner works effectively for fixed order DG as well as p-adaptive DG problems. Finally, with the improvements provided by the p-adaptivity and AMG preconditioning, we can perform high resolution three-dimensional viscous fingering simulations required for miscible displacement with high Peclet number and mobility ratio in greater detail than before for well injection problems.},
doi = {10.1016/j.jcp.2018.07.003},
journal = {Journal of Computational Physics},
number = ,
volume = 374,
place = {United States},
year = {2018},
month = {7}
}

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