Adaptive enriched Galerkin methods for miscible displacement problems with entropy residual stabilization

Lee, Sanghyun; Wheeler, Mary F.

doi:10.1016/j.jcp.2016.10.072

Title: Adaptive enriched Galerkin methods for miscible displacement problems with entropy residual stabilization

Journal Article · Wed Nov 23 00:00:00 EST 2016 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2016.10.072· OSTI ID:1533954

^[1]; Wheeler, Mary F. ^[1]

University of Texas, Austin, TX (United States)

Here we present a novel approach to the simulation of miscible displacement by employing adaptive enriched Galerkin finite element methods (EG) coupled with entropy residual stabilization for transport. In particular, numerical simulations of viscous fingering instabilities in heterogeneous porous media and Hele–Shaw cells are illustrated. EG is formulated by enriching the conforming continuous Galerkin finite element method (CG) with piecewise constant functions. The method provides locally and globally conservative fluxes, which are crucial for coupled flow and transport problems. Moreover, EG has fewer degrees of freedom in comparison with discontinuous Galerkin (DG) and an efficient flow solver has been derived which allows for higher order schemes. Dynamic adaptive mesh refinement is applied in order to reduce computational costs for large-scale three dimensional applications. In addition, entropy residual based stabilization for high order EG transport systems prevents spurious oscillations. Numerical tests are presented to show the capabilities of EG applied to flow and transport.

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Research Organization:: Univ. of Texas, Austin, TX (United States)

Sponsoring Organization:: USDOE Office of Science (SC); Statoil; Aramco

Grant/Contract Number:: FG02-04ER25617; STNO-4502931834,UTA 11-000320; UTA 11-000320; STNO-4502931834

OSTI ID:: 1533954

Alternate ID(s):: OSTI ID: 1397822

Journal Information:: Journal of Computational Physics, Vol. 331, Issue C; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 38 works

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97 MATHEMATICS AND COMPUTING
enriched Galerkin finite element methods
miscible displacement
viscous fingering
locally conservative methods
entropy viscosity
Hele–Shaw

Title: Adaptive enriched Galerkin methods for miscible displacement problems with entropy residual stabilization

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