Both analytical and numerical results are employed to compare the accuracy of numerical methods for the solution of the system of nonlinear partial differential equations that represent the conservation of mass, momentum, and energy in thermal-hydraulic codes. The analysis points out the types of errors that need to be addressed to make the conservation of mass, momentum, and energy in thermal-hydraulic codes more accurate. Simulation results depict trends that are expected from the analytical results. Conclusions based on both the analytical and numerical results show that modern numerical methods can provide significant improvements in accuracy over the approaches employed in the current thermal-hydraulic codes.