Finite volume approximation of a diffusion–dissolution model and application to nuclear waste storage

Angelini, O.; Chavant, Clément; Chénier, Eric; Eymard, Robert; Granet, S.

doi:10.1016/j.matcom.2010.12.016

Cited by 30 publications

(34 citation statements)

References 10 publications

(18 reference statements)

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“…Alternately, we also consider the case of Richards' equation, which can be obtained from (1) in two ways. One can replace (1a) by u(x, t) =ū(x) for (x, t) ∈ Ω × (0, T ),…”

Section: (φ(X)s(x P(x T))∂ T ϕ(X T) + K 2 (X S(x P(x T)))λ(x)(∇mentioning

confidence: 99%

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Gradient schemes for two‐phase flow in heterogeneous porous media and Richards equation

Eymard¹,

Guichard

Herbin

et al. 2013

Z Angew Math Mech

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The gradient scheme family, which includes the conforming and mixed finite elements as well as the mimetic mixed hybrid family, is used for the approximation of Richards equation and the two-phase flow problem in heterogeneous porous media. We prove the convergence of the approximate saturation and of the approximate pressures and approximate pressure gradients thanks to monotony and compactness arguments under an assumption of non-degeneracy of the phase relative permeabilities. Strong convergence results stem from the convergence of the norms of the gradients of pressures, which demand handling the nonlinear time term. Numerical results show the efficiency on these problems of a particular gradient scheme, called the Vertex Approximate Gradient scheme.

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“…Alternately, we also consider the case of Richards' equation, which can be obtained from (1) in two ways. One can replace (1a) by u(x, t) =ū(x) for (x, t) ∈ Ω × (0, T ),…”

Section: (φ(X)s(x P(x T))∂ T ϕ(X T) + K 2 (X S(x P(x T)))λ(x)(∇mentioning

confidence: 99%

“…The existence of a weak solution to Problem (1), under various hypotheses, is studied in [2,8,12,20] for example. Some mathematical results of convergence have been obtained for several approximations of this problem.…”

Section: (φ(X)s(x P(x T))∂ T ϕ(X T) + K 2 (X S(x P(x T)))λ(x)(∇mentioning

confidence: 99%

Gradient schemes for two‐phase flow in heterogeneous porous media and Richards equation

Eymard¹,

Guichard

Herbin

et al. 2013

Z Angew Math Mech

Self Cite

View full text Add to dashboard Cite

show abstract

“…From remarks 1 and 2, a one parameter family of independent on x Robin coefficients L, M i , i = a, w, N can be obtained using L > 0 as a real parameter and setting (17), (19), (22). We deduce that independent on x Robin coefficients can be competitive for this test case and also that our computation almost reaches the optimal number of iterations of this one parameter family.…”

Section: Andra Test Casementioning

confidence: 61%

“…Following [19,20], our choice of the liquid gas Darcy flow formulation uses the pressures p g , p of both phases, the vector f = (f i ) i∈C of the component fugacities and the temperature, denoted by T pm in the porous medium, as primary unknowns.…”

Section: Nonisothermal Compositional Darcy Flow In the Porous Mediummentioning

confidence: 99%

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A domain decomposition method to couple nonisothermal compositional gas liquid Darcy and free gas flows

Birgle

Masson

Trenty

2018

Journal of Computational Physics

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A domain decomposition algorithm is introduced to couple nonisothermal compositional gas liquid Darcy and free gas flow and transport. At each time step, our algorithm solves iteratively the nonlinear system coupling the nonisothermal compositional Darcy flow in the porous medium, the RANS gas flow in the free-flow domain, and the transport of the species and of energy in the free-flow domain. In order to speed up the convergence of the algorithm, the transmission conditions at the interface are replaced by Robin type boundary conditions. The Robin coefficients are obtained from a diagonal approximation of the Dirichlet to Neumann operator related to a simplified model in the neighbouring subdomain. The efficiency of our domain decomposition algorithm is assessed on several test cases focusing on the modeling of the mass and energy exchanges at the interface between the geological formation and the ventilation galleries of geological radioactive waste disposal.

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Numerical simulation of gas migration through engineered and geological barriers for a deep repository for radioactive waste

Amaziane

Ossmani

Jurak

2012

Comput. Visual Sci.

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cited By (since 1996)0International audienceIn this paper a finite volume method approach is used to model the 2D compressible and immiscible two-phase flow of water and gas in heterogeneous porous media. We consider a model describing water-gas flow through engineered and geological barriers for a deep repository of radioactive waste. We consider a domain made up of several zones with different characteristics: porosity, absolute permeability, relative permeabilities and capillary pressure curves. This process can be formulated as a coupled system of partial differential equations which includes a nonlinear parabolic gas-pressure equation and a nonlinear degenerated parabolic water-saturation equation. Both equations are of diffusion-convection type. An implicit vertex-centred finite volume method is adopted to discretize the coupled system. A Godunov-type method is used to treat the convection terms and a conforming finite element method with piecewise linear elements is used for the discretization of the diffusion terms. An averaging technique is developed to obtain an effective capillary pressure curve at the interface of two media. Our numerical model is verified with 1D semi-analytical solutions in heterogeneous media. We also present 2D numerical results to demonstrate the significance of capillary heterogeneity in flow and to illustrate the performance of the method for the FORGE cell scale benchmark. © 2013 Springer-Verlag Berlin Heidelberg

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Finite volume approximation of a diffusion–dissolution model and application to nuclear waste storage

Cited by 30 publications

References 10 publications

Gradient schemes for two‐phase flow in heterogeneous porous media and Richards equation

Gradient schemes for two‐phase flow in heterogeneous porous media and Richards equation

A domain decomposition method to couple nonisothermal compositional gas liquid Darcy and free gas flows

Numerical simulation of gas migration through engineered and geological barriers for a deep repository for radioactive waste

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