In this study, we introduce the Delft Advanced Research Terra Simulator (DARTS), which employs the Operator-Based Linearization (OBL) approach to provide efficient and precise solutions for non-linear discretized equations, to simulate the polymer flooding process. This compositional simulation framework is feasible for describing complex physical phenomenon with high nonlinearity because detached functional operators have been developed to release the calculation load while maintaining a high degree of stability and accuracy. The main contributions and innovations are shown below: i. A two-phase and three-component chemical flooding mathematical model with some reasonable assumptions was developed to investigate the enhanced-oil-recovery (EOR) mechanism of polymer flooding. A finite volume discretization scheme and a fully implicit method (FIM) are implemented to approximate the conservation equations. The OBL approach is used to reduce the complexity of the simulation framework. The correctness of the model is verified by comparison with analytical model. ii. In addition to shear thinning effect, polymer viscoelasticity has also been taken into account. This mathematical model is able to handle high shear rates during field displacement as well as low to medium shear rates in laboratory experiments. iii. A new model for porosity reduction caused by polymer adsorption is formulated. The effect of polymer concentration on the effective pore volume is incorporated in numerical simulations based on Langmuir adsorption model.