A dynamic grid point allocation scheme for the Characteristic Finite Difference Method

Codes for predicting the events which can occur during a reactor loss-of-coolant accident (LOCA) must be able to cope with the essentially steady flows of normal operation and long-term cooling, as well as with the very severe transients occurring during the blowdown and water injection phases. Although large timesteps and a coarse grid are adequate for steady flows, smaller timesteps and a finer grid are necessary to preserve accuracy during the fast transients. The RAMA code, based on the characteristic finite difference method, has a dynamic grid point allocation scheme which helps to control spatial truncation error. In this scheme, grid points are inserted in regions where large spatial gradients occur in the flow-boiling variables and are deleted when these gradients subside. As well, the mesh of grid points is free to move with the gradients. The algorithm used is similar to that for dynamic timestep control, where large temporal gradients in the flow-boiling variables dictate small timesteps and larger timesteps are used for shallower gradients. The goal is to maintain a prescribed accuracy in the calculation during the entire LOCA prediction while using the minimum number of grid points at each step and, in total, the minimum number of timesteps. Examples are presented which demonstrate the computational efficiency of the scheme, including a benchmark problem involving cold water injection and an experimental case involving both blowdown and cold water injection phases