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

Sesini, Paula A.; Souza, Denis A. F. de; Coutinho, Álvaro L. G. A.

doi:10.1590/s1678-58782010000300013

Cited by 16 publications

(5 citation statements)

References 35 publications

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“…Over the last two decades, the continuum equations that govern viscous fingering have been solved in the literature using many different numerical methods including finite volume [4,16], spectral [17,18], and continuous and discontinuous Galerkin finite element (FEM) [19][20][21][22] as well as mixed control volume finite element (CVFEM) [23,24]. Early work focussed on the use of higher order numerical schemes in association with finite volume methods to ensure that physical diffusion dominated over numerical diffusion [4,16].…”

Section: Introductionmentioning

confidence: 99%

Dynamic adaptive mesh optimisation for immiscible viscous fingering

et al. 2020

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Immiscible fingering is challenging to model since it requires a very fine mesh for the numerical method to capture the interaction of the shock front with the capillary pressure. This can result in computationally intensive simulations if a fixed mesh is used. We apply a higher order conservative dynamic adaptive mesh optimisation (DAMO) technique, to model immiscible viscous fingering in porous media. We show that the approach accurately captures the development and growth of the interfacial instability. Convergence is demonstrated under grid refinement with capillary pressure for both a fixed unstructured mesh and with DAMO. Using DAMO leads to significantly reduced computational cost compared to the equivalent fixed mesh simulations. We also present the late-time response of viscous fingers through numerical examples in a 2D rectangular domain and in a 3D cylindrical geometry. Both problems are computationally challenging in the absence of DAMO. The dynamic adaptive problem requires up to 36 times fewer elements than the prohibitively expensive fixed mesh solution, with the computational cost reduced accordingly.Keywords Immiscible viscous fingering · Dynamic adaptive mesh optimisation · Double control volume finite element method

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Section: Introductionmentioning

confidence: 99%

Dynamic adaptive mesh optimisation for immiscible viscous fingering

et al. 2020

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“…Sesini also studied the effects of anisotropy using linear and radial Hele-Shaw setups considering high mobility ratios, up to 106 [ 73 ]. The model used by Sesini was based on the mathematical formulation developed by Coutinho [ 63 ].…”

Section: Modeling Of Vf At the Microscale: 2d And 3d Simulationsmentioning

confidence: 99%

Experimental and computational advances on the study of Viscous Fingering: An umbrella review

Pinilla

Asuaje²,

Ratkovich

2021

Heliyon

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“…The work of Johnson et al [33], Bassi and Rebay [7], and Hartmann and Houston [24], successfully demonstrate the use of residual-based artificial viscosity to control oscillations in finite element solutions of the compressible Euler equations. Similar residual-based methods have been applied to miscible displacement and three-phase flow problems in [50,49]. The entropy viscosity method introduced in [22] stabilizes the solution by adding an artificial viscosity that is proportional to the entropy residual, and is demonstrated for nonlinear scalar conservation laws and the Euler equations using a continuous Galerkin (CG) method.…”

Section: Artificial Viscositymentioning

confidence: 99%

Upwinding and artificial viscosity for robust discontinuous Galerkin schemes of two-phase flow in mass conservation form

et al. 2020

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is demonstrated on a two-phase flow problem with heterogeneous rock permeabilities, where the high-order discretizations significantly outperform a conventional first-order approach in terms of computational cost required to achieve a given level of error in an output of interest.Keywords two-phase flow • discontinuous Galerkin • linear stability • upwinding • artificial viscosity • high-order

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

Abstract: Numerical simulations of viscous fingering instabilities in miscible displacements

Cited by 16 publications

References 35 publications

Dynamic adaptive mesh optimisation for immiscible viscous fingering

Dynamic adaptive mesh optimisation for immiscible viscous fingering

Experimental and computational advances on the study of Viscous Fingering: An umbrella review

Upwinding and artificial viscosity for robust discontinuous Galerkin schemes of two-phase flow in mass conservation form

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