Stabilized finite element methods with reduced integration techniques for miscible displacements in porous media

Abstract

SUMMARYThe objective of this work is to study some techniques to increase computational performance of stabilized finite element simulations of miscible displacements. We propose the use of a reduced integration technique for bilinear quadrilateral elements in the determination of the pressure and concentration fields. We also study the evaluation of pressure gradient (Darcy's velocity) by differentiation at superconvergent points. Numerical examples are shown to validate our approach, accessing its efficiency and accuracy.

Reduced integration post‐processing techniques for Darcy's velocity recovery in bilinear quadrilaterals

“…Some stabilization techniques are effective in avoiding hourglass modes, and its control is still a topic of current research, see, for example, [14][15][16][17][18] and the references therein. A reduced integration scheme that is able to produce good solutions for convective and/or diffusive problems was studied in [9]. This scheme is an extension of the original method proposed in [14] for diffusive problems, in which the main idea was to add to the element matrix evaluated by one-point Gaussian quadrature, stabilization terms derived through the Hu-Washizu variational formulation.…”

“…The motivation here is to extend the scheme introduced in [9] to increase computational performance of finite element simulations of miscible displacements with bilinear quadrilaterals. Dias and Coutinho [9] proposed the use of a reduced integration technique for bilinear quadrilateral elements in the determination of pressure and concentration fields and the evaluation of pressure gradient (Darcy's velocity) by differentiation at superconvergent points. They have shown by numerical experiments that for regular meshes it is not necessary to explicitly enforce superconvergence of the velocity field.…”

Dynamics of a Highly Viscous Circular Blob in Homogeneous Porous Media

“…Its wide applicabilities, e.g., enhanced oil recovery [1], CO 2 sequestration [2], chromatographic separation [3,4], contaminant transport in aquifers [5], mixing in low-Reynolds number flow [6], intrinsic characteristics of nonlinear dynamics and pattern formation have fascinated active theoretical, numerical [6][7][8][9][10][11][12][13], and experimental [14] researchers for more than half a decade. Both rectilinear and radial displacements have been investigated rigorously and have their own significance that can be investigated independently as well as comparatively.…”

Finite element simulation of viscous fingering in miscible displacements at high mobility-ratios

“…Many authors Homsy, 1993, 1995;Moissis et al, 1987;Singh and Azaiez, 2001;Tan andHomsy, 1986, 1988) consider more convenient and efficient to work in terms of vorticity and streamfunction. Alves (1996, 1999), Loula et al (1999), Dias and Coutinho (2004), , Patzek (2002, 2004) employ primitive variables: pressure, velocity and concentration.…”

“…In this work, we study the ability of the formulation (Coutinho and Alves, 1996;Dias and Coutinho, 2004;) described above to simulate some very high mobility-ratio displacement processes (MR = exp(6)). At this time, we use two different geometries: a rectilinear Hele-Shaw cell and a radial case, where we use unstructured grids.…”