This paper investigates the performance of a commercially available computational fluid dynamics (CFD) solver (Ansys FLUENT) to predict the flow and heat transfer characteristics of a two-phase closed thermosyphon (TPCT). Specifically, the study compares two different discretization schemes for the volume fraction equation with different time step sizes using three different sets of mass transfer time relaxation parameters for evaporation and condensation. The present study evaluates use of the Compressive scheme to increase the time step size compared to the Geo-Reconstruct scheme. In addition, a model is proposed to adjust the global saturation temperature of the system based on the volume of the vapor phase in order to balance the mass transfer inside TPCT and more accurately represent the realistic operating conditions of a TPCT. In this study a total of nineteen simulations are performed, and two types of boundary conditions for the condenser are investigated to determine the effect on the accuracy of the simulation results. The baseline simulation uses the Geo-Reconstruct method with a fixed saturation temperature. Other additional cases are performed using the Geo-Reconstruct method with variable saturation temperature, and the Compressive method with and without variable saturation temperature using different sets of mass transfer time relaxation parameters. Results show that the case using the Compressive method with the variable saturation temperature model has good agreement with the reference experimental data and is less computationally expensive than the Geo-Reconstruct method. The 3D CFD models implemented in this study successfully predict the phase change process and flow behavior inside the TPCTs, at least in a qualitative sense.