In this article, a numerical solution of incompressible two-phase flow in isothermal condition, based on wetting pressure-wetting saturation formulation (Pw,Sw) using high order primal discontinuous Galerkin (DG) methods is considered which can capture the shock fronts of two-phase flow in heterogeneous porous media. In this presented model, the velocity field is reconstructed by a H(div) post-process in lowest order of Raviart-Thomas space (RT0). Also in this study, the scaled penalty and weighted average (harmonic average) formulation significantly improve the especial discretization formulation of governing equations which cause to reduce the instabilities in heterogamous media. The modified MLP slope limiter is used to remove the non-physical saturation values at end of each time step. In this study, the slope limiter should be considered as one of the main novelties due to the impressive effects in results stabilization. The proposed model is verified by pseudo 1D Buckley-Leverett and Mcwhorter problems. Two test cases, a problem for modeling the secondary recovery of petroleum reservoirs and other one a problem for detecting immiscible contamination are used to show the abilities of shock capturing two phases interface in porous media.

Keywords: two-phase flow, local conservation, Slope limiter, discontinuous Galerkin method, Interior penalty

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