Development of a parallel analytic coarse mesh finite difference code for two group diffusion equation solution in two dimensional rectangular geometries

Highlights: •Two dimensional diffusion equation in two energy group was solved using ACMFD method. •Most time consuming sections in ACMFD algorithm were identified. •OpenMP library was used to implement parallelism in ACMFD method. •An analysis of the number of processors in parallel solution process was done. •A feasible and optimum parallel computing code (P-ACMFD) for reactor core calculation was provided. -- Abstract: In this work we have developed a parallel analytic coarse mesh finite difference (P-ACMFD) code for two group and two dimensional diffusion calculations of eigenvalue problems. The first part in this paper is to describe the conventional ACMFD method. The solution procedure involves three steps. The first step is to reduce the coupled system of the 2 group diffusion equations to the 2 independent modal equations in the eigenspaces of the 2 × 2 matrix. The second step is to apply the transverse leakage integration to X–Y plane geometry and third step is to solve analytically the resultant one dimensional equation in each direction. Verification results for ACMFD method are provided, corresponding to the light water reactor benchmark problem. As a second part, OpenMP was used to implement parallelism in ACMFD. OpenMP is a standard Application Programming Interface for writing shared memory parallel applications in C++. The main structure of P-ACMFD code consists of three different computing modules. The code execution time dominantly depends on computing time of each of them. Then, adequacy and parallel efficiency of the provided P-ACMFD code was demonstrated based on some cases.