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Title

Convergence of Implicit Monotone Schemes with Applications in Multiphase Flow in Porous Media

Authors
Tchelepi, Hamdi A.
Published in SIAM Journal on Numerical Analysis. 2008, vol. 46, no. 5, p. 2662-2687
Abstract Phase-based upstreaming, which is a commonly used spatial discretization for multiphase flow in reservoir simulation, naturally gives rise to implicit monotone schemes when implicit time-stepping is used. The nonlinear Gauss–Seidel and Jacobi algorithms are shown to converge to a unique bounded solution when applied to the resulting system of equations. Thus, for one-dimensional problems, we obtain an alternate, constructive proof that such schemes are well-defined and converge to the entropy solution of the conservation law for arbitrary CFL numbers. The accuracy of phase-based upstream solutions is studied for various spatial and temporal grids, revealing the importance of unconditional stability when nonuniform grids and/or variable porosity is involved.
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KWOK, Wing Hong Félix, TCHELEPI, Hamdi A. Convergence of Implicit Monotone Schemes with Applications in Multiphase Flow in Porous Media. In: SIAM Journal on Numerical Analysis, 2008, vol. 46, n° 5, p. 2662-2687. https://archive-ouverte.unige.ch/unige:8542

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Deposited on : 2010-07-02

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