Neutron kinetics plays an important role in reactor safety and analysis. The backward Euler method is the most widely used time integration method in the calculation of space-dependent nuclear reactor kinetics. Diagonally Implicit Runge-Kutta (DIRK) method owns high accuracy and excellent stability and it could be applied to the neutron kinetics for hexagonal-z geometry application. As solving the neutron kinetics equations is very time-consuming and the number of available cores continues to increase with parallel architectures evolving, parallel algorithms need to be designed to utilize the available resources effectively. However, it is difficult to parallel in time axis since the later moment is strongly dependent on the previous moment. In this paper, the Parareal method which is a time parallel method and implemented by MPI in the processor level is studied in the hexagonal-z geometry with the help of DIRK method. In order to make good use of the parallelism, a parallel strategy in the space direction is also used. In the coarse nodal method, many same operations are finished in the nodes and these operations could be parallel by OpenMP in the thread level since they are independent. Several transient cases are used to validate this method. The results show that the Parareal method gets a fast-convergent speed such as only 2∼3 iterations are needed to convergent. This space-time parallel method could reduce the cost time compared to the sequential method.
Modified parareal method for solving the two-dimensional nonlinear shallow water equations using finite volumes
