Deterministic Neutron Transport Methods Development at Imperial College for the FETCH Transient Crit

1

• Deterministic Neutron Transport Methods
  Development at Imperial College for the FETCH
  Transient Criticality Modelling Framework

Matthew Eaton, Christopher Pain, Andrew Buchan,
Tony Goddard, Mike Williams, Matthew Piggott,
Jefferson Gomes, Brendan Tollit, Jason Dunstall
and Andrew Hague
2
Deterministic Neutron Transport Methods
Development

• Discretisation methods development
• Angular discretisation development
• Solver developments
• Conclusions and future/current work

3
Deterministic Neutron Transport Methods
Development

• Spatial Discretisation methods
• Past methods such as even-parity unreliable for
  treating voids and highly absorbing problems.
• New methods such as SUPG, DG and CVFEM robust
  across spectrum of radiation regimes using linear
  and non-linear methods.
• Space-time solvers for robust time-dependent
  solutions.
• Current emphasis with AWE on robust DG based
  schemes.
• All Implemented with the RADIANT radiation
  transport framework

4
Deterministic Neutron Transport Methods
Development

• Angular discretisation methods
• A new Riemann based approach that enables
  arbitrary angular discretisation methods.
• Spherical harmonics
• Discrete ordinates
• Walsh functions
• Wavelets
• New anisotropically self-adaptive formulations
  using Wavelets
• All Implemented with the RADIANT radiation
  transport framework

5
Deterministic Neutron Transport Methods
Development
Octahedral and hexahedral wavelets
Level 0
Level 1
Level 2
6
Wavelet test case
110 angular basis functions used on average from
a possible 612 wavelets
7
Wavelet test case
P1204 wavelets
P2 288 wavelets
P3 322 wavelets
P4 286 wavelets
8
Wavelet test case
P5 224 wavelets
P6 204 wavelets
P7 183 wavelets
9
Algebraic multigrid solver

• Solve the maximal independent set problem
• Assign Finite elements to coarse elements
• Map the spatial information onto the coarse grid
  using the restriction operator

10
Algebraic multigrid solver test problem
Exact solution
Iteration 2MG
Iteration 3MG
Iteration 3SSOR
Iteration 1
Iteration 2SSOR
11
Conclusions

• Further work on RADIANT includes
• Developing goal based error metrics for space,
  angle, time and energy adaptivity.
• Parallelisation of RADIANT
• Uncertainty propagation methods
• Integration of RADIANT into FETCH framework