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In this paper, we consider an online enrichment procedure using theGeneralized Multiscale Finite Element Method (GMsFEM) in the context of atwo-phase flow model in heterogeneous porous media. The coefficient of theelliptic equation is referred to as the permeability and is the main source ofheterogeneity within the model. The elliptic pressure equation is solved usingonline GMsFEM, and is coupled with a hyperbolic transport equation where localconservation of mass is necessary. To satisfy the conservation property, we aimat constructing conservative fluxes within the space of multiscale basisfunctions through the use of a postprocessing technique. In order to improvethe accuracy of the pressure and velocity solutions in the online GMsFEM weapply a systematic online enrichment procedure. The increase in pressureaccuracy due to the online construction is inherited by the conservative fluxfields and the desired saturation solutions from the coupled transportequation. Despite the fact that the coefficient of the pressure equation isdependent on the saturation which may vary in time, we may construct anapproximation space using the initial coefficient where no further basisupdates follow. Numerical results corresponding to four different types ofheterogeneous permeability coefficients are exhibited to test the proposedmethodology.

Online conservative generalized multiscale finite element method for flow models