Semi-classical solutions for a nonlinear coupled elliptic-parabolic problem

Choquet, Catherine

doi:10.1017/s0004972700039757

Cited by 4 publications

(2 citation statements)

References 33 publications

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“…However, the investigated benchmarks involve Dirichlet or Neumann boundary conditions. Thus, developing new benchmarks with different types of boundary conditions [31,32] is worth further investigations. Table A2.…”

Section: Discussionmentioning

confidence: 99%

On the Validity of the Null Current Assumption for Modeling Sorptive Reactive Transport and Electro-Diffusion in Porous Media

Tabrizinejadas

Carrayrou

Saaltink

et al. 2021

Water

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In multispecies electrolyte solutions, each individual species can migrate according to its specific ionic properties. This process is called electrochemical migration or electro-diffusion and is well-described by the Nernst–Planck equation. The common approach for solving the corresponding mathematical system is based on the null current (NC) assumption, which expresses the electric potential in terms of charges and concentrations of chemical components. This assumption has a great advantage as it eliminates the electric potential from the Nernst–Planck equation. However, the NC assumption has limited capacities in describing electro-diffusion processes when the domain is subjected to an external electric field. The validity of the NC assumption could be questionable, even in the absence of an external electric field. This topic has never been investigated in the past. The main goal of this work is to evaluate the validity of the NC assumption and to understand its effect on the model outputs. Thus, we present a new reactive transport model that allows for a reliable representation of the electrochemical migration process. This model is based on the Nernst–Planck and Poisson (NPP) equations which are solved together. We also implement a model based on the NC assumption. Both models have been validated by comparison with CrunchFlow, based on several benchmarks. The results show that in the case of high sorptivity, the NC assumption is no longer valid. Therefore, in the case of sorption processes, the NPP should be used to simulate coulombic interactions.

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Section: Discussionmentioning

confidence: 99%

On the Validity of the Null Current Assumption for Modeling Sorptive Reactive Transport and Electro-Diffusion in Porous Media

Tabrizinejadas

Carrayrou

Saaltink

et al. 2021

Water

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show abstract

“…We refer the reader to [3] for a numerical approach to the problem. We also mention that in [5] the author investigated regularity properties of solutions to a problem similar to ours.…”

Section: Xiangsheng Xumentioning

confidence: 91%

Partial regularity for an elliptic-parabolic system modeling miscible fluid flows in porous media

2024

DCDS

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Strong solutions for Richards’ equation with Cauchy conditions and constant pressure gradient

Berardi

Difonzo

2019

Environ Fluid Mech

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Semi-classical solutions for a nonlinear coupled elliptic-parabolic problem

Cited by 4 publications

References 33 publications

On the Validity of the Null Current Assumption for Modeling Sorptive Reactive Transport and Electro-Diffusion in Porous Media

On the Validity of the Null Current Assumption for Modeling Sorptive Reactive Transport and Electro-Diffusion in Porous Media

Partial regularity for an elliptic-parabolic system modeling miscible fluid flows in porous media

Strong solutions for Richards’ equation with Cauchy conditions and constant pressure gradient

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