Non-Fickian convection–diffusion models in porous media

In this paper we propose a numerical scheme to approximate the solution of a non-Fickian coupled model that describes, e.g., miscible transport in porous media. The model is defined by a system of a quasilinear elliptic equation, which governs the fluid pressure, and a quasilinear integro-differenti...

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Bibliographic Details
Published inNumerische Mathematik Vol. 138; no. 4; pp. 869 - 904
Main Authors Barbeiro, Sílvia, Bardeji, Somayeh Gh, Ferreira, José A., Pinto, Luís
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2018
Springer Nature B.V
Subjects
Approximation
Differential equations
Finite element method
Fluid pressure
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical and Computational Physics
Porous materials
Porous media
Simulation
Theoretical
Transport processes
65 M12
65M60
65N06
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Summary:In this paper we propose a numerical scheme to approximate the solution of a non-Fickian coupled model that describes, e.g., miscible transport in porous media. The model is defined by a system of a quasilinear elliptic equation, which governs the fluid pressure, and a quasilinear integro-differential equation, which models the convection–diffusion transport process. The numerical scheme is based on a conforming piecewise linear finite element method for the discretization in space. The fully discrete approximations is obtained with an implicit–explicit method. Estimates for the continuous in time and the fully discrete methods are derived, showing that the numerical approximation for the concentrations and the pressure are second order convergent in a discrete L 2 -norm and in a discrete H 1 -norm, respectively.
ISSN:0029-599X
0945-3245
DOI:10.1007/s00211-017-0922-6