In the last few years, the analysis of thermal-hydraulic behavior in reactor systems has been conducted by using the best-estimate codes. In order to provide realistic predictions of nuclear power plant (NPP) systems, the best-estimate codes employ numerous numerical methods and physical models. In the nuclear system analysis code such as RELAP5, MARS and TRACE, the governing equations are solved by the 1st order numerical scheme in both space and time discretization. However, the 1st order numerical scheme on the fixed mesh can yield excessive numerical diffusion problem. So, the non-conservative results can be predicted for analyzing transients with steep spatial or temporal gradient of physical parameters. In the analysis of the nuclear system, the major challenge is to capture the sharp peak or the dramatic changes with sufficient accuracy while also keeping the computational cost reasonably low. This study conducts the mesh sensitivity analysis with the conventional 1st order numerical scheme and the higher-order numerical schemes by simulating the subcooled boiling conditions. Since the subcooled boiling phenomena occur due to the thermally non-equilibrium state, many complicated phenomena such as bubble generation, bubble departure, bubble growth and condensation are involved. Therefore, this study conducts the simulation of the subcooled boiling conditions using the developed code for the concept validation and mesh sensitivity tests.