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Combined Mixed-Hybrid Finite Element–Finite Volume Scheme for Computation of Multicomponent Compressible Flow in Porous Media

In: Numerical Mathematics and Advanced Applications 2011

Author

Listed:
  • O. Polívka

    (Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Department of Mathematics)

  • J. Mikyška

    (Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Department of Mathematics)

Abstract

The paper deals with the numerical modeling of compressible single-phase flow of a mixture composed of several components in a porous medium. The mathematical model is formulated by Darcy’s law, components continuity equations, constitutive relations, and initial and boundary conditions. The problem is solved numerically using a combination of the mixed-hybrid finite element method for the total flux discretization and the finite volume method for the discretization of the transport equations. The time discretization is carried out by Euler’s method. The resulting large system of nonlinear algebraic equations is solved by the Newton-Raphson method. The dimensions of the obtained system of linear algebraic equations are significantly reduced so that they do not depend on the number of mixture components. The convergence of the numerical scheme is verified in the single-component case by comparing the numerical solution with an analytical solution.

Suggested Citation

  • O. Polívka & J. Mikyška, 2013. "Combined Mixed-Hybrid Finite Element–Finite Volume Scheme for Computation of Multicomponent Compressible Flow in Porous Media," Springer Books, in: Andrea Cangiani & Ruslan L. Davidchack & Emmanuil Georgoulis & Alexander N. Gorban & Jeremy Levesley (ed.), Numerical Mathematics and Advanced Applications 2011, edition 127, pages 559-567, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-33134-3_59
    DOI: 10.1007/978-3-642-33134-3_59
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