Application of Lax-Wendroff scheme in 1D nuclear system analysis code

Abstract

In the last few years, the analysis of thermal-hydraulic behavior in reactor systems has been conducted by using the best-estimate codes such as RELAP5, MARS-KS and TRACE. These codes employ the 1st order numerical scheme in both space and time discretization, which can occur the excessive numerical diffusion problem near steep spatial or temporal gradient of physical parameters. To reduce the numerical diffusion and satisfy Courant number limitation, the nodalization becomes more important in the 1st order numerical scheme. However, since it is impossible to set ideal node configuration while modeling a complex system such as NPP, the numerical diffusion problem cannot be avoided in the 1st order numerical scheme and this issue can be overcome with higher order numerical scheme. In this thesis, it is shown that the accuracy can be improved and the nodalization uncertainty can be reduced by improving the current numerical scheme. To evaluate the accuracy and nodalization uncertainty for the 1st order upwind scheme and Lax-Wendroff scheme, MARS-KS code is revised to use both 1st order upwind scheme and Lax-Wendroff scheme. The analysis of the accuracy and nodalization uncertainty is performed for the separate effect tests (SETs) such as subcooled boiling, critical flow, counter-current flow limitation, and reflood experiments. Furthermore, the Lax-Wendroff scheme is tested for the APR1400 LBLOCA case to evaluate the ability for reducing the nodalization uncertainty and improving the performance. In this thesis, the revised MARS-KS code, which uses Lax-Wendroff scheme, shows that improved accuracy and more consistent results can be predicted by reducing the numerical diffusion problem in general. However, it is also found that phenomena such as critical flow and CCFL are less affected by the higher order numerical scheme due to its unique way of treating the momentum governing equation. Moreover, the improvement of the Lax-Wendroff scheme can cost up to 10 times more calculation time. Therefore, it is necessary to develop a method accelerate the calculation time while maintaining similar accuracy and sensitivity to the nodalization in order to predict the NPP behavior more accurately under fast transients.