Temporal oscillations in the simulation of foam enhanced oil recovery

Meer, Jitse M. van der; Kraaijevanger, J.B.F.M.; Möller, Matthias

doi:10.3997/2214-4609.201601850

Cited by 6 publications

(21 citation statements)

References 6 publications

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“…Figures 4a and 5a depict that in the former refinement results in higher frequencies and lower amplitudes, whereas in the latter the amplitude does not decrease. Figures 4b and 5b show that the formation of a temporal oscillation coincides with the time when the front crosses a grid cell [4]. Finer grids consist of more grid cells, explaining the higher frequency oscillations present.…”

Section: Numerical Artifacts In the 1d Pmementioning

confidence: 93%

“…The degeneracy of the GPME poses interesting numerical challenges and, if care is not taken, locking, lagging and temporal oscillations can result [1][2][3][4]. These numerical artifacts are distinct from the typical sharp gradient challenges caused by dispersive errors in hyperbolic conservation laws (see Section 2).…”

Section: Strategies To Overcome the Numerical Artifacts In Discretizamentioning

confidence: 99%

“…This discontinuous GPME is challenging and has led to several other approaches, e.g. the integral average in [4].…”

Section: Strategies To Overcome the Numerical Artifacts In Discretizamentioning

confidence: 99%

“…For applications in reservoir simulations, where the governing equation is parabolic with variable coefficients, arithmetic averaging can result in overly diffusive profiles and nonphysical solutions with flow allowed in and out of impermeable layers [2]. Also, arithmetic averaging does not always remove the temporal oscillations, as seen in [4,13] for the GPME with discontinuous k(p) (Eqn. (1.4)).…”

Section: Strategies To Overcome the Numerical Artifacts In Discretizamentioning

confidence: 99%

“…We discuss how to discretize the self-sharpening Generalized Porous Medium Equation (GPME) without the temporal oscillations, the locking, and the lagging reported in previous works [1][2][3][4]. In these works, the numerical artifacts have been attributed to harmonic averaging, and arithmetic averaging has been proposed to resolve them.…”

Section: Introductionmentioning

confidence: 99%

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Numerical artifacts in the Generalized Porous Medium Equation: Why harmonic averaging itself is not to blame

Maddix

Sampaio

Gerritsen

2018

Journal of Computational Physics

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The degenerate parabolic Generalized Porous Medium Equation (GPME) poses numerical challenges due to selfsharpening and its sharp corner solutions. For these problems, we show results for two subclasses of the GPME with differentiable k(p) with respect to p, namely the Porous Medium Equation (PME) and the superslow diffusion equation. Spurious temporal oscillations, and nonphysical locking and lagging have been reported in the literature. These issues have been attributed to harmonic averaging of the coefficient k(p) for small p, and arithmetic averaging has been suggested as an alternative. We show that harmonic averaging is not solely responsible and that an improved discretization can mitigate these issues. Here, we investigate the causes of these numerical artifacts using modified equation analysis. The modified equation framework can be used for any type of discretization. We show results for the second order finite volume method. The observed problems with harmonic averaging can be traced to two leading error terms in its modified equation. This is also illustrated numerically through a Modified Harmonic Method (MHM) that can locally modify the critical terms to remove the aforementioned numerical artifacts.

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Section: Numerical Artifacts In the 1d Pmementioning

confidence: 93%

Section: Strategies To Overcome the Numerical Artifacts In Discretizamentioning

confidence: 99%

“…This discontinuous GPME is challenging and has led to several other approaches, e.g. the integral average in [4].…”

Section: Strategies To Overcome the Numerical Artifacts In Discretizamentioning

confidence: 99%

Section: Strategies To Overcome the Numerical Artifacts In Discretizamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Numerical artifacts in the Generalized Porous Medium Equation: Why harmonic averaging itself is not to blame

Maddix

Sampaio

Gerritsen

2018

Journal of Computational Physics

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Numerical artifacts in the discontinuous Generalized Porous Medium Equation: How to avoid spurious temporal oscillations

Maddix¹,

Sampaio²,

Gerritsen³

2018

Journal of Computational Physics

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Numerical discretizations of the Generalized Porous Medium Equation (GPME) with discontinuous coefficients are analyzed with respect to the formation of numerical artifacts. In addition to the degeneracy and self-sharpening of the GPME with continuous coefficients, detailed in [1], increased numerical challenges occur in the discontinuous coefficients case. These numerical challenges manifest themselves in spurious temporal oscillations in second order finite volume discretizations with both arithmetic and harmonic averaging. The integral average, developed in [2], leads to improved solutions with monotone and reduced amplitude temporal oscillations. In this paper, we propose a new method called the Shock-Based Averaging Method (SAM) that incorporates the shock position into the numerical scheme. The shock position is numerically calculated by discretizing the theoretical speed of the front from the GPME theory. The speed satisfies the jump condition for integral conservation laws. SAM results in a non-oscillatory temporal profile, producing physically valid numerical results. We use SAM to demonstrate that the choice of averaging alone is not the cause of the oscillations, and that the shock position must be a part of the numerical scheme to avoid the artifacts.

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