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Deterministic Neutron Transport Methods Development at Imperial

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					      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
    Deterministic Neutron Transport Methods
                  Development


•   Discretisation methods development
•   Angular discretisation development
•   Solver developments
•   Conclusions and future/current work
 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
 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
 Deterministic Neutron Transport Methods
               Development
Octahedral and hexahedral wavelets




 Level 0                Level 1      Level 2
                    Wavelet test case




110 angular basis functions used on average from a possible 612 wavelets
                       Wavelet test case




P1:204 wavelets   P2: 288 wavelets   P3 322 wavelets   P4: 286 wavelets
                   Wavelet test case




P5: 224 wavelets      P6: 204 wavelets   P7: 183 wavelets
Algebraic multigrid solver

                    1. Solve the maximal
                       independent set
                       problem
                    2. Assign Finite elements
                       to coarse elements
                    3. Map the spatial
                       information onto the
                       coarse grid using the
                       restriction operator
  Algebraic multigrid solver test problem




Exact solution    Iteration 2:MG     Iteration 3:MG




                                    Iteration 3:SSOR
  Iteration 1    Iteration 2:SSOR
                 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

				
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