Applied problems of oil and gas recovery are studied numerically using the mathematical models of multiphase fluid flows in porous media. The basic model includes the continuity equations and the Darcy laws for each phase, as well as the algebraic expression for the sum of saturations. Primary computational algorithms are implemented for such problems using the pressure equation. In this paper, we highlight the basic properties of the pressure problem and discuss the necessity of their fulfillment at the discrete level. The resulting elliptic problem for the pressure equation is characterized by a non-selfadjoint operator. Possibilities of approximate solving the elliptic problem are considered using the iterative methods. Special attention is given to the numerical algorithms for calculating the pressure on parallel computers.
Vabishchevich, P., & Vasil’eva, M. (2012). Iterative solution of the pressure problem for the multiphase filtration. Mathematical Modelling and Analysis, 17(4), 532-548. https://doi.org/10.3846/13926292.2012.706655
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