- Thesis (M.S., Mechanical Engineering) -- University of Idaho, December 2014 | RELAP5 is based on a two-fluid, non-equilibrium, non-homogeneous, hydrodynamic model for the transient simulation of the two-phase flow system behavior. In current versions of RELAP5, the "non-conservative" numerical approximation form is used. For discretization of the non-conservative form, the truncation errors introduced in the linearization process can produce mass and energy errors for some classes of transients during time advancements, either resulting in (a) automatic reduction of time steps used in the advancement of the equations and increased run times or (b) the growth of unacceptably large errors in the transient results. To eliminate these difficulties, a more conservative numerical approach has been introduced and implemented into RELAP5/SCDAP. This article demonstrates the theory of both the non-conservative and the developed conservative numerical approach. It also introduces the solution strategy of the more conservative approach and presents the code-to-code comparison between the non-conservative and more conservative approaches. RELAP5/SCDAP mode 4.0 versions are utilized for the code-to-code comparisons. These comparisons results prove that mass error is significantly reduced by implementing the more conservative numerical approximation.