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International Conference on Numerical Analysis and Its Applications

NAA 2012: Numerical Analysis and Its Applications pp 379–386Cite as

Finite Volume Approximations for Incompressible Miscible Displacement Problems in Porous Media with Modified Method of Characteristics

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8236))

Abstract

The incompressible miscible displacement problem in porous media is modeled by a coupled system of two nonlinear partial differential equations, the pressure-velocity equation and the concentration equation. The pressure-velocity is elliptic type and the concentration equations is convection dominated diffusion type. It is known that miscible displacement problems follow the natural law of conservation and finite volume methods are conservative. Hence, in this paper, we present a mixed finite volume element method (FVEM) for the approximation of the pressure-velocity equation. Since concentration equation is convection dominated diffusion type and most of the numerical methods suffer from the grid orientation effect and modified method of characteristics(MMOC) minimizes the grid orientation effect. Therefore, for the approximation of the concentration equation we apply a standard FVEM combined MMOC. A priori error estimates are derived for velocity, pressure and concentration. Numerical results are presented to substantiate the validity of the theoretical results.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Space Science and Technology, Thiruvananthapuram, 695 547, Kerala, India

    Sarvesh Kumar

Authors
  1. Sarvesh Kumar
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Editor information

Editors and Affiliations

  1. Institute of Information and Communication Technlogies, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl25A, 1113, Sofia, Bulgaria

    Ivan Dimov

  2. Department of Applied Analysis, Pázm\’{a}ny P\’{e}ter s\’{e}t\’{a}ny 1/C,, Eötvös Loránd University, 1117, Budapest, Hungary

    István Faragó

  3. University of Rousse, 8 Studentska Str.,, 7017, Rousse, Bulgaria

    Lubin Vulkov

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Kumar, S. (2013). Finite Volume Approximations for Incompressible Miscible Displacement Problems in Porous Media with Modified Method of Characteristics. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2012. Lecture Notes in Computer Science, vol 8236. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41515-9_42

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  • DOI: https://doi.org/10.1007/978-3-642-41515-9_42

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41514-2

  • Online ISBN: 978-3-642-41515-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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