To meet the new engine regulations, increasingly sophisticated engine alternative combustion modes have been developed in order to achieve simultaneously the emission regulations and the required engine drivability. However, these new approaches require more complex, reliable and precise control systems and technologies. The 0-D model based control systems have proved to be successful in many applications, but as the complexity of the engines increases, their limitations start to affect the engine control performance. One of the 0-D modeling limitations is their inability to model mass transport time. 1-D modeling allows some of the 0-D models limitations to be overcome, which is the motivation of this work. In this paper, two quasi-steady outflow boundary models are developed: one is based on the isentropic contraction and the other on a momentum conservation approach. Both are compared with computational fluid dynamics (CFD) 3-D simulations. Then, an innovative method for solving the outflow boundary problem taking into account the entropy correction at the boundary for a 1-D unsteady gas flow modeling is presented. Its formulation allows more predictive quasi-steady models to be included in the boundary resolution scheme by solving the boundary problem independently of the restriction model. It means that a physical restriction model can be modified without needing to change the boundary resolution method. A Newton-Raphson algorithm is used with a modified Method of Characteristics (MOC) scheme to solve the boundary problem along with an extrapolation for the initialization of the scheme, which reduces the amount of iterations required and increases the solution accuracy. The unsteady behavior of the method is illustrated in an engine intake valve example where the numerical performance of the proposed method is compared with the numerical scheme presented in the literature. Finally, the proposed method for solving the unsteady state is validated using 3-D CFD simulations as a reference.