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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:331

Article

Lee, Sanghyun¹  Wheeler, Mary F.¹ 

[1] Univ Texas Austin, Inst Computat Engn & Sci, Ctr Subsurface Modeling, Austin, TX 78712 USA

关键词: Enriched Galerkin finite element methods;    Miscible displacement;    Viscous fingering;    Locally conservative methods;    Entropy viscosity;    Hele-Shaw;   

DOI  :  10.1016/j.jcp.2016.10.072

来源: Elsevier

【 摘 要 】

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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free