1. I-2. Power Method and Wielandt Shift II. Multigroup Neutron Diffusion
Reactor Numerical Analysis and Design 1st Semester of 2008
Lecture Note 2
I-2. Power Method and Wielandt Shift II. Multigroup Neutron Diffusion
March 11, 2008
Prof. Joo Han-gyu
Department of Nuclear Engineering

2. Power Method

3. Power Method with Scaling

4. Convergence of Power Method with Scaling

5. Inverse Power method

6. LU factorization

7. Convergence of Power method

8. Wielandt Eigenvalue Shift Method

9. Wielandt Shift Method for Neutronic EigenValue Problem

10. Determination of Eigenvalue in Wielandt Shift

11. Reduction in Dominance Ratio with Wielandt Shift

12. II. 1-D, Multigroup Neutron Diffusion Problem

13. Discretization at boundary

14. Ordering scheme ① Group Major Ordering ② Node Major Ordering
primary sort variable : Group (g)
secondary sort variable : Node (k)
② Node Major Ordering
primary sort variable : Node (k)
secondary sort variable : Group (g)

15. Matrix Structure with Node Major Ordering Scheme

16. Matrix Structure in Node Major Ordering Scheme

17. Matrix structure in Node major ordering scheme
Area NOT having Fission

18. Matrix Structure in Group Major Ordering Scheme

19. Fission Matrix Structure in Group Major

20. Scattering Matrix Structure in Group Major Ordering

21. Matrix Structure According to Ordering Scheme
Node Major
Group Major
Interior
Scattering Shape
Tri diagonal matrix
Exterior
Scattering Shape
Problem to Fit
A Few Group Problem (2G)
Many Group Problem

22. Source Iteration for Group Major Ordering

23. Iterative Multigroup Solution Algorithm
Loop for outer iteration step i
1) Determine fission source at each node and fission source adjustment parameter
Loop over groups
2) Determine source at each node for the current group
3) Solve for flux for the group
4) Determine new fission source
5) Estimate new k
6) Estimate pseudo error
7) Estimate Dominance Ratio
8) Check Convergence and Exit outer if convergence is met else go (1)

24. Nested Iteration Flow Chart (when upscattering present)
Group Sweep (Middle)
Pseudo Error

25. Problem with Wielandt Shift for MG