On High Order Numerical Schemes for 1-D Fluid Model

摘要

In this work, we have successfully demonstrated that second order accuracy could be achieved for both time and space for thermal hydraulics analyses with 1-D single-phase problems, utilizing the Newton-Krylov nonlinear solving method. Two grid arrangements to achieve high-resolution solutions have been tested and compared. The 2nd order staggered grid upwind scheme demonstrates its advantages as it is easier to implement and more flexible to handle equation system in both conservative and primitive forms. It is also flexible to handle ill-posed equation systems, as it does not need to compute the local characteristic speeds. However, it is well known that the ill-posed equation system, such as the two-fluid two-phase model commonly used in the nuclear thermal hydraulics field, relies on the numerical diffusion to 'regulate' its ill-posedness. It is not clear when higher order of accuracy schemes are used, how the ill-posedness could be regulated. We would leave this to our future studies to investigate the two-phase model behaviors using higher order schemes.