Dr. V. H. Sánchez Espinoza

victor.sanchez@kit.edu

+49 72160822283

Dr. K. Zhang

kanglong.zhang@kit.edu

+49 72160822544

Topic: Theoretical investigation on the convergence behavior of the Super-Homogenisation (SPH) method, particularly for PARCS solution procedures
Duration: 6 Months
Requirements: Nuclear Physics, Numerical methods, Mathematical Physics, Linear algebra
Location: KIT Campus North, Institute for Neutron Physics and Reactor Technology (INR), Reactor Physics and Dynamics Division (RPD), Building 521

Contact persons:
Dr. Victor Hugo Sánchez Espinoza (victor.sanchez@kit.edu, +49 72160822283)
Dr. Kanglong Zhang (kanglong.zhang@kit.edu, +49 72160822544)

Description: Motivation/ Background:
As to the neutronic simulation approach, people usually use lattice codes or Monte-Carlo codes to generate few group constants e.g. the Cross Section (XS). Then they apply the XS to diffusion solvers to perform the simulation with acceptable computational costs. However, the diffusion solutions are not as good as that of the Monte-Carlo codes despite the XS from the Monte-Carlo solutions. Thus, the Super-Homogenisation (SPH) method was initiated to refine the XS for the diffusion codes. It is to preserve the neutron reaction rates between the diffusion and Monte-Carlo solutions. The SPH is an iteration technique. Its convergence behavior is a fundamental aspect to be analyzed. However, the reason for the SPH convergence has not been revealed, though the SPH method was proved effective and has many successful applications. The theoretical demon-stration of the SPH convergence would complete the full picture of the SPH method. Here in KIT-INR-RPD, we focus mostly on the SPH method associated with the eigenvalue problem of the diffusion solver - PARCS.

Goals of the internship:
The main goal of the internship is to reveal the convergence behavior of the SPH method (an iteration tech-nique) associated with the eigenvalue problem of PARCS, from the theoretical perspective.

Work program:
- Literature review about PARCS, the SPH method.
- Investigating the theory of the neutronic solvers in PARCS, especially the Steady State eigenvalue solver.
- Investigating the SPH convergence behavior theoretically.
- Write a final report and presentation.