One-dimensional two-phase generalized Forchheimer flows of incompressible fluids

Hoang, Luan; Ibragimov, Akif; Kieu, Thinh

doi:10.1016/j.jmaa.2012.12.055

Cited by 12 publications

(19 citation statements)

References 15 publications

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“…These equations are analyzed numerically in [7,19,27], theoretically in [2,[10][11][12][13]16] for single-phase flows, and also in [14,15] for two-phase flows. Our previous analysis [2,[10][11][12][13]16] was focused on a simplified model for slightly compressible fluids.…”

Section: Introductionmentioning

confidence: 99%

Generalized Forchheimer Flows of Isentropic Gases

Çelik

Hoang

Kieu

2017

J. Math. Fluid Mech.

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We consider generalized Forchheimer flows of either isentropic gases or slightly compressible fluids in porous media. By using Muskat's and Ward's general form of the Forchheimer equations, we describe the fluid dynamics by a doubly nonlinear parabolic equation for the appropriately defined pseudo-pressure. The volumetric flux boundary condition is converted to a time-dependent Robin-type boundary condition for this pseudo-pressure. We study the corresponding initial boundary value problem, and estimate the L ∞ and W 1,2−a (with 0 < a < 1) norms for the solution on the entire domain in terms of the initial and boundary data. It is carried out by using a suitable trace theorem and an appropriate modification of Moser's iteration.

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Section: Introductionmentioning

confidence: 99%

Generalized Forchheimer Flows of Isentropic Gases

Çelik

Hoang

Kieu

2017

J. Math. Fluid Mech.

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“…It is used to unify the models (1.2), (1.3), (1.4), and as a framework for interpretation of different experimental or field data. It is analyzed numerically in [8,21,27], theoretically in [2,[12][13][14][15]18] for single-phase flows, and also in [16,17] for two-phase flows. For compressible fluids, especially gases, the dependence of coefficients a i 's on the density ρ is essential.…”

Section: Introductionmentioning

confidence: 99%

Doubly nonlinear parabolic equations for a general class of Forchheimer gas flows in porous media

2018

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This paper is focused on the generalized Forchheimer flows of compressible fluids in porous media. The gravity effect and other general nonlinear forms of the source terms and boundary fluxes are integrated into the model. It covers isentropic gas flows, ideal gases and slightly compressible fluids. We derive a doubly nonlinear parabolic equation for the so-called pseudopressure, and study the corresponding initial boundary value problem. The maximum estimates of the solution are established by using suitable trace theorem and adapting appropriately the Moser's iteration. The gradient estimates are obtained under a theoretical condition which, indeed, is relevant to the fluid flows in applications.

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“…These equations are analyzed numerically in [7][8][9], theoretically in [4,6,[10][11][12][13] for single phase flows, and also in [14,15] for two-phase flows.…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis for generalized Forchheimer flows of slightly compressible fluids

Kieu

2017

Numerical Methods Partial

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In this article, we will consider the generalized Forchheimer flows for slightly compressible fluids. Using Muskat's and Ward's general form of Forchheimer equations, we describe the fluid dynamics by a nonlinear degenerate parabolic equation for density. The long-time numerical approximation of the nonlinear degenerate parabolic equation with time dependent boundary conditions is studied. The stability for all time is established in a continuous time scheme and a discrete backward Euler scheme. A Gronwall's inequalitytype is used to study the asymptotic behavior of the solution. Error estimates for the solution are derived for both continuous and discrete time procedures. Numerical experiments confirm the theoretical analysis regarding convergence rates. K E Y W O R D SDarcy-Forchheimer flow, error analysis, Galerkin FEM, nonlinear degenerate parabolic equations, numerical analysis

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One-dimensional two-phase generalized Forchheimer flows of incompressible fluids

Cited by 12 publications

References 15 publications

Generalized Forchheimer Flows of Isentropic Gases

Generalized Forchheimer Flows of Isentropic Gases

Doubly nonlinear parabolic equations for a general class of Forchheimer gas flows in porous media

Numerical analysis for generalized Forchheimer flows of slightly compressible fluids

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