Performance evaluation of higher-order numerical scheme for application of 1D nuclear system analysis code

Abstract

The existing nuclear system analysis codes such as RELAP5, TRAC, MARS and SPACE use the 1st order numerical scheme in both space and time discretization to solve the governing equations. However, the numerical diffusion problem can be occurred in the 1st order numerical scheme. Nowadays, the nuclear system analysis code requires higher accuracy for the prediction of the thermal margin in the nuclear system. Therefore, a nuclear system analysis code with better performance is needed for both nuclear industry and regulatory activities. Thus, this study evaluated the applicability of the higher-order numerical schemes for the next generation nuclear system analysis code. In this study, single phase pipe flow simulation with a sine pulse of temperature was conducted to evaluate the accuracy and the maximum Courant number of the 1st order and 2nd order numerical schemes. For the 2nd order numerical schemes, the 2nd order upwind scheme, centered differencing scheme and Lax-Wendroff scheme are used. The 2nd order backward Euler scheme is used for the temporal numerical scheme. So, the sensitivity of the higher order numerical schemes is conducted in terms of the improvement of the accuracy and the change of the maximum Courant number for the stability. Also, the effect of the numerical diffusion and dispersion is evaluated by comparing the theoretical and the calculated maximum Courant number of each higher order numerical scheme. Furthermore, these attempts should be identified whether more stable and accurate solutions can be obtained under the two phase flow conditions in the future.