Nuclear Science and Engineering / Volume 151 / Number 2 / October 2005 / Pages 212-223
As an efficiency enhancement numerical scheme of transient nonlinear nodal calculations, a three-grid correction scheme (3GCS) using a modified W cycle based on three grid structures of three-dimensional (3-D) four-node-per-assembly (4N/A), 3-D 1N/A, and two-dimensional (2-D) 1N/A is developed. Its computational efficiency is compared with a single-grid biconjugate gradient stabilized (BICGSTAB) iteration scheme in popular use in terms of 3-D 4N/A nonlinear analytical nodal method solutions to Nuclear Energy Agency Committee on Reactor Physics pressurized water reactor rod ejection benchmark problems. It is shown that in computational efficiency, the 3GCS excels the BICGSTAB iteration method using preconditioners such as Jacobi, incomplete lower and upper (ILU), and 3-D block incomplete lower and upper (BILU3D) preconditioners. It is also shown that coarse-grid residual equations based on the 3-D 1N/A grid structure can predict temporal truncation errors as accurately as the 3-D 4N/A fine-grid residual equation but with considerably less overhead computing time for variable time-step size control calculations by a step doubling method. In addition, incorporation of preconditioners into the 3GCS is shown to enhance further efficiency of the nonpreconditioned 3GCS. From these results, it is concluded that the temporal adaptive 3GCS employing coarse-grid residual equations for temporal step-size control as well as the preconditioner like the BILU3D can provide a very efficient iterative solution scheme for transient nonlinear nodal calculations.