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

Journal Article · · Journal of Computational Physics
 [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)

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.

Research Organization:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); ExxonMobil Upstream Research Company, Spring, TX (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
Report Number(s):
SAND-2018-9819J; 667674
Journal Information:
Journal of Computational Physics, Vol. 374; ISSN 0021-9991
ElsevierCopyright Statement
Country of Publication:
United States
Citation Metrics:
Cited by: 5 works
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Web of Science