In many oil recovery processes, water-based EOR methods are considered with added polymer component into the water to reduce the viscous instability and improve recovery efficiency. Efficient and accurate numerical simulation of the displacement processes is critical for predictions of injectivity and recovery profiles.

A linear spectral finite volume method for multi-component multi-phase polymer flow and transport in porous media is presented in this work. The reduced-dimensional discrete fracture model is also considered for fractured porous media. This work couples the linear spectral finite volume methods with the control-volume distributed multi-point flux approximations (CVD-MPFA) methods on triangular grids in 2D geometry resulting in improved efficiency for several aspects, including velocity and flux computations, and several Riemann solvers have also been compared for their performances. The results demonstrate the improved efficiency and accuracy of the spectral finite volume methods.