Steps involved in the development and application of numerical reservoir simulator models to primary and secondary recovery processes in reservoir engineering. Model formulation, General Material Balances, Single Phase flow, Overall Program Structure, Finite difference Approximations, finite Element Approximations, Boundary and Initial Conditions, Well Model, Anisotropy, Error, Grid Selection, Stability Analysis, Non-linear Problems, Multiphase Flow Models, IMPES Solution, Simultaneous Solution, Stability of Multiphase Flow FDEs, Reservoir Framework, Relative Permeability, Transmissibility in Multiphase Flow Effective Relative Permeability, Capillary-gravity Equilibrium, Model Initialization, Reservoir Characterization.