Study on application of higher-order numerical scheme to 1-D thermal-hydraulic system analysis code

Abstract

The existing nuclear system analysis codes such as RELAP5, TRAC, MARS and SPACE use the first-order numerical scheme in both space and time discretization. However, the first-order scheme is highly diffusive and less accurate due to the first order of truncation error. Nowadays, the nuclear system analysis code requires higher accuracy for the prediction of the nuclear system safety and therefore, a nuclear reactor system analysis code with better performance is needed in nuclear industry. Thus, this study evaluated the application of the higher-order numerical scheme for the next generation nuclear system analysis code. In this study, to identify effects of numerical diffusion and dispersion problem and the decreasing error depending on the increasing mesh number, single phase pipe flow simulation with a sine pulse of temperature was conducted. The calculation was performed with MARS and a separate single phase transient analysis code, namely NTS code, which is possible to calculate in the first-order and the higher-order schemes but mimics MARS solver built in MATLAB environment. In addition, to evaluate sensitivity of the results to the input perturbation in the first-order and second-order schemes, simplified primary loop of nuclear reactor system simulation was performed by MARS and NTS codes. Through this study, the numerical diffusion and dispersion problems in the numerical methods were observed in a single phase transient analysis code. In addition, it is identified that the numerical diffusion and dispersion problems result in numerical instabilities and non-physical solutions. Therefore, to stabilize the numerical solutions of the higher-order scheme and to obtain more precise solutions, a slope limiter should be applied or more stable higher-order scheme should be implemented. Furthermore, these attempts should be identified whether more stable and accurate solutions can be obtained under the two phase flow conditions in the future.