Abstract
Two-phase incompressible fluid flow through highly heterogeneous porous media is simulated by using the Multiscale Finite Volume (MsFV) method. Effects of the localization assumption on the accuracy of the MsFV are investigated by comparing the results associated with different boundary conditions of local problems producing the basis functions. The total number of six boundary conditions of two general types, including Dirichlet and Dirichlet-Neumann types, are compared. For the former, the linear, variable (reduced), and step-type boundary conditions are considered and a modified variable boundary condition is proposed. For the latter, a basic and a step-type Neumann-Dirichlet boundary condition are suggested. To estimate the errors in the MsFV solutions for continuous problems, a heterogeneous two-dimensional problem with continuous permeability field is designed and solved analytically. Synthetic two-scale permeability fields as well as highly heterogeneous random fields are used to assess the accuracy of the MsFV solutions with different localization schemes, in comparison with the fine-scale reference solution. Numerical results indicate that the modified variable boundary condition, with a proper value of its weighting factor, can generally produce the most accurate results, when compared with the other localization schemes.
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