The generalized finite volume SUSHI scheme for the discretization of the peaceman model

Mohamed Mandari; Mohamed Rhoudaf; Ouafa Soualhi

Applications of Mathematics (2021)

  • Volume: 66, Issue: 1, page 115-143
  • ISSN: 0862-7940

Abstract

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We demonstrate some a priori estimates of a scheme using stabilization and hybrid interfaces applying to partial differential equations describing miscible displacement in porous media. This system is made of two coupled equations: an anisotropic diffusion equation on the pressure and a convection-diffusion-dispersion equation on the concentration of invading fluid. The anisotropic diffusion operators in both equations require special care while discretizing by a finite volume method SUSHI. Later, we present some numerical experiments.

How to cite

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Mandari, Mohamed, Rhoudaf, Mohamed, and Soualhi, Ouafa. "The generalized finite volume SUSHI scheme for the discretization of the peaceman model." Applications of Mathematics 66.1 (2021): 115-143. <http://eudml.org/doc/297030>.

@article{Mandari2021,
abstract = {We demonstrate some a priori estimates of a scheme using stabilization and hybrid interfaces applying to partial differential equations describing miscible displacement in porous media. This system is made of two coupled equations: an anisotropic diffusion equation on the pressure and a convection-diffusion-dispersion equation on the concentration of invading fluid. The anisotropic diffusion operators in both equations require special care while discretizing by a finite volume method SUSHI. Later, we present some numerical experiments.},
author = {Mandari, Mohamed, Rhoudaf, Mohamed, Soualhi, Ouafa},
journal = {Applications of Mathematics},
keywords = {porous medium; nonconforming grid; finite volume scheme; a priori estimate; miscible fluid flow},
language = {eng},
number = {1},
pages = {115-143},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The generalized finite volume SUSHI scheme for the discretization of the peaceman model},
url = {http://eudml.org/doc/297030},
volume = {66},
year = {2021},
}

TY - JOUR
AU - Mandari, Mohamed
AU - Rhoudaf, Mohamed
AU - Soualhi, Ouafa
TI - The generalized finite volume SUSHI scheme for the discretization of the peaceman model
JO - Applications of Mathematics
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 1
SP - 115
EP - 143
AB - We demonstrate some a priori estimates of a scheme using stabilization and hybrid interfaces applying to partial differential equations describing miscible displacement in porous media. This system is made of two coupled equations: an anisotropic diffusion equation on the pressure and a convection-diffusion-dispersion equation on the concentration of invading fluid. The anisotropic diffusion operators in both equations require special care while discretizing by a finite volume method SUSHI. Later, we present some numerical experiments.
LA - eng
KW - porous medium; nonconforming grid; finite volume scheme; a priori estimate; miscible fluid flow
UR - http://eudml.org/doc/297030
ER -

References

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