Abstract
A cell-centered multigrid method is presented for the solution of the system of differential equations used to model multiphase flow in a porous medium. We have applied the cell-centered multigrid method as a linear solver both to the symmetric set of equations arising from an IMPES formulation and to the unsymmetric coupled set of equations that comes from a fully implicit formulation.
In the fully implicit case the system of nonlinear equations is solved by Newton iterations. The cell-centered multigrid method works well even in the case of jump discontinuities in the coefficients. This method avoids using special interpolation operators for multigrid transfers based on the discretized differential equation. Useful properties as conservation of mass is conserved by this scheme. Results of numerical experiments are presented.
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Teigland, R., Fladmark, G.E. (1991). Cell-centered Multigrid Methods in Porous Media Flow. In: Hackbusch, W., Trottenberg, U. (eds) Multigrid Methods III. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 98. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5712-3_27
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DOI: https://doi.org/10.1007/978-3-0348-5712-3_27
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