Abstract
We introduce some numerical approximations to a quasilinear problem proposed by G. I. Barenblatt to describe non-equilibrium two-phase fluid flows in permeable porous media, which apply to secondary oil recovery from natural reservoirs. Taking into account the theoretical results of global existence and uniqueness, we approximate the solutions by three numerical schemes, namely, the Diagonal First Order schemes (DFO and DF02) and the Diagonal Second Order scheme (DSO). For DFO schemes convergence is proved. The schemes' behaviour is analysed and discussed through some numerical experiments.
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