STABILITY IMPROVEMENT OF THE ALTERNATING DIRECTION IMPLICIT METHOD FOR 2-DIMENSIONAL SPACE-TIME REACTOR KINETICS APPLICATIONS

The alternating direction implicit (ADI) method has been widely used to obtain numerical solutions of the two-dimensional time-dependent, multigroup neutron diffusion equations. However, the conventional ADI method is unstable for heterogeneous problems unless extremely small time steps are used. Recently, the suitability of the ADI method for parallel computation has been noted since it is based on the solution of a system of independent block-tridiagonal matrix equations that can be solved in parallel. More precisely, on a computer with p processors, p members of the tridiagonal system can be solved in parallel using the well-known Gaussian elimination algorithm. By improving the stability of the ADI method, the method becomes extremely attractive for parallel computer applications. A mixed implicit-explicit three-level ADI method for the solution of the two-dimensional multigroup diffusion equations is introduced. Mixed implicit-explicit methods are usually more effective than purely explicit or implicit procedures for the solution of stiff equations and, for the type of problem considered, lead to a demonstrated stability improvement over the conventional ADI method. Numerical studies using the MADI program, which implements the three-level ADI method, show that by using the same time-step size, the method obtains results that are almost as accurate as those of the TWIGL program in about one-third to one-fourth the computational time for both homogeneous and heterogeneous two-group problems.