1. Comparison of Recently Developed Deterministic Codes with Applications
Update and Progress on Deterministic-Based Neutronics
Comparison of Recently Developed Deterministic Codes with Applications
Mahmoud Z Youssef
UCLA
FNST/PFC/MASCO Meetings, August 2-6, 2010, University of California, Los Angeles

2. Outlines -Backgroud information
- Method of Discrete Ordinates (discretization in energy, angle and space)
- History of of issuance of deterministic codes
Recently developed deterministic codes and comparison
- Denovo - PARTISN - ATTILA
Applications (Capabilities and Limitations) – Emphasize on Attila
Comments

3. Calculation Methods for Neutron and Photon Transport
The methods can be broken down into two broad groups
Deterministic method:
Directly solves the equation using numerical techniques for solving a system of ordinary and partial differential equations
Monte Carlo method:
Solves the equation using probabilistic and statistical techniques (Stochastic Approach)
Each method has its strengths and weaknesses

4. Deterministic Method: Linear Boltzmann Transport Equation (LBTE)
streaming
collision
sources
where,
Represents a particle balance over a differential control volume:
Streaming + Collision = Scattering Source + Fixed Source
No particles lost

5. Angular Discretization
Angular Differencing – Discrete Ordinates (SN)
Solves the transport equation by sweeping the mesh on discrete angles defined by a quadrature set which integrates the scattering source
Sweeps the mesh for each angle in the quadrature set Ωi
0.5 cm Element Size
SN=Quadrature set of order N Number of angles in level-symmetric set= N(N+2)
Abdou Lecture 5

6. Scattering Source Expansion
Scattering cross section is represented by expansion in Legendre Polynomials
The angular flux appearing in the scattering source is expanded in Spherical Harmonics
The degree of the expansion of the resulting scattering source is referred to as the PN expansion order
Flux moments
Spherical Harmonics
PN=Harmonics expansion approximation  number of moments=(N+1)2
Abdou Lecture 5

7. Energy Discretization
Division of energy range into discrete groups (Muti-groups):
Multigroup constants are obtained by flux weighting, such as
This is exact if is known a priori
Highly accurate solutions can be obtained with approximations for by a spectral weighting function

8. Spatial Discretization
Traditional SN approaches use regular orthogonal structured grid (2D,3D)
Regular Cartesian or polar grids
Cell size driven by smallest solution feature requiring resolution
Many elements are required (several millions)
curved boundaries are approximated by orthogonal grid
Advanced SN approaches use unstrctured tetrahedral cells (3D)
Cell sized can be controlled at pre-selected locations.
Highly localized refinement for capturing critical solution regions
Much fewer elements needed for accurate solution
curved boundaries are accurately represented
0.5 cm Element Size
Orthogonal structured Grid
Unstructured grid

9. Number of the Unknowns in Discrete Ordinates Method
number of unknowns per cell
Number of Energy groups
NT= Nc x n x t x Nu x Ng
Number of spatial cells
Number of angles =N(N+2) (SN )
Number of moments= (L+1)2 (PL )
For a typical of Ni=Nj=Nk=400, S32, P3 , Ng=67 (orthogonal grid)
NT x unknown
In unstructured tetrahedral grid
NT= ~5 x ( 2 orders of magnidude less)

10. History of Deterministic Discrete Ordinates Codes
Development of the deterministic methods for nuclear analysis goes back to the early 1960:
OakRidge National Laboratory (ORNL):
(1D) W. Engle: ANISN (1967)
(2D) R.J. Rogers , W.W. Engle, F.R. Mynatt, W.A. Rhoades, D.B. Simpson, R.L. Childs, T Evans: DOT (1965), DOT II (1967), DOT III (1969), DOT3.5 (1975), DOT IV (1976)……… DORT (~1997)
(3D) TORT (~1997))…….DOORS (early 2000)… DENOVO ~2007-to date)
Los Alamos National Laboratory (LANL):
K.D. Lathrop, F.W. Brinkley, W.H. Reed, G.I. Bell, B.G. Carlson, R. E. Alcouffe, R. S. Baker, J. A. Dahl: TWOTRAN (1970), TWOTRAN II (1977) ….THREETRAN…… …TRIDENT-CTR(~1980)……DANTSYS (1995)…PARTISN (2005) 10
ATTILA: 3D-FEM-unstrctured tetrahedral cells (1995). Now Transpire/UC

11. Spatial Descritization:
Comparison of Recent Discrete Ordinates Codes 1/5
Spatial Descritization:
Orthogonal and structured:
- Weighted diamond differencing (Denovo, PARTISN)
Weighted diamond differencing with linear-zero fixup (Denovo, PARTISN)
- Adaptive weighted diamond Differencing (PATISN)
- Linear discontinuous Galerkin finite element (Denovo, PRTISN)
- Trilinear-discontinuous Galerkin finite element (Denovo)
Exponential discontinuous finite element (PARTISN)
- Step characteristics, slice balance (Denovo)
Arbitrary and Unstructured:
- Tri-linear discontinuous Finite Element (DFEM) on an arbitrary tetrahedral mesh (ATTILA)

12. Parallelization Method Inner Iteration Method
Comparison of Recent Discrete Ordinates Codes 1/5
Parallelization Method
- Koch-Baker-Alcouffe (KBA) parallel-wavefront sweeping algorithm (Denovo)
- 2-D spatial decomposition (and inversion of source iteration equation in a single sweep (PARTISN)
Spatial decomposition parallelism (ATTILA)
Iteration Method
- Krylov method (within-group, non-stationary method) (Denovo)
- Source iteration (stationary) method (PARTISN, ATTILA)
Inner Iteration Method
Diffusion synthetic acceleration, DSA (All)
Transport synthetic acceleration (TSA) (All)

13. Denovo: Parallel 3-D Discrete Ordinates Code
Denovo serves as the deterministic solver module in the SCALE MAVRIC sequence
SCALE
MAVRIC
Denovo
CADIS
Appropriate Weight windows
Sn- 3-D Code
Geom. Model
Monaco with Automated Variance Reduction using Importance Mapping- Monte Carlo Code
Consistent Adjoint Driven Importance Sampling
.Developed to replace TORT as the principal 3-D deterministic transport code for nuclear technology applications at Oak Ridge National Laboratory (ORNL).

14. Application of Denovo: PWR
Denovo is used extensively on the National Center for Computational Sciences (NCCS) Cray XT5 supercomputer (Jaguar).
The KBA method (direct inversion, parallel sweeping) allows for good weak-scaling on Jaguar.
This ability to run massive problems in reasonable runtimes
Slightly more than 1 hr
Over 1 Billion mesh
10 cm mesh size
From: Thomas M. Evans , “Denovo-A New Parallel Discrete Transport Code for Radiation Shielding Applications”
Transport Methods Group, Oak Ridge National Laboratory, One Bethel Valley Rd, Oak Ridge, TN 37831

15. ATTILA
A finite element Sn neutron, gamma and charged particle transport code using 3D unstructured grids (tetrahedral meshes)
Geometry input from CAD (Solid Works, ProE)
ATTILA R&D Started at LANL (1995) by CIC-3 Group.
Currently being maintained through an exclusive license agreement between Transpire Inc. and University of California..
Shared memory parallel version SEVERIAN
Accepted as an ITER design tool in July, 2007

16. Generic Diagnostic Upper Port Plug Neutronics
Section Through Upper Port
Showing the Visible/IR Camera Labyrinth
W/cm3
Generic Upper Port Nuclear Heating
Total: 316 kW
First Wall + Diagnostic Shield: 309 kW
GUPP Structure: 7 kW
Generic Upper Port Plug
SolidWorks Analysis Model

17. Generic Diagnostic Upper Port Plug Neutronics
Vacuum
Flange
ATTILA
Simplified representation of the Generic Diagnostic Upper Port Structure
ANSYS
Thermal Analysis in ANSYS
Based on Nuclear Heating
Data from ATTILA

19. Alite04-UCLA ITER Reference CAD Model
40-degree 1:1 scale CAD model re-centered around the lower RH divertor port.
Contains all components and is fully compliant with the Alite03 and Alite04 Diverter model furnished by ITER IO**
M12 upper port connections from the ATTILA Alite04 model of UKAEA Culham.
Many cleanup and minor modifications suitable for nuclear analysis were performed in SolidWorks and ANSYS.
 Meshed by Attila
Model will be sent to ITER IO and made available to neutronics community
**This work was carried out using an adaptation of the Alite MCNP model which was developed as a collaborative effort between the FDS team of ASIPP China, ENEA Frascati, JAEA Naka, UKAEA Culham and the ITER Organisation

20. Neutron Flux in the Vacuum Vessel
Looking down: Horizontal cut at Mid-plane
Bottom of VV

21. Neutron Heating
Gamma Heating
W/cc
Total Heating is dominated by gamma heating

23. Accumulated Dose (Gy) in the Epoxy Insulator at 0.3 MW.a/m2
Diagnostics and Port shield Installed
3.67E4
1.67E6
2.01E6
9.02E4
PF4
PF4
Magnet Insulator
PF5
PF5
PF6
PF6
3E3
Diagnostics/shield not installed
Dose in PF5 reduced by a factor of 100 when divertor port is plugged
Dose limit of 10 MGy is not reached
Local Insulator Dose: The dose limit to the insulation is 10MGy
Dose (Gy/s) = Heating (W/cc)*1/ρmaterial*1000g/kg
Local Lifetime Limit 10 MGy, Assume Titer_life = 1.7E7 seconds

24. TBM (2)
Shield
Cryostat
Bio-shield
AEU
Port Inter space area
Youssef Dagher
Dose rates in the port inters pace and AEU area need
Assessment → acurate ocupational Radiation Exposure (ORE) rates

25. We have a meashable ITER model with DCLL TBM inserted

26. Follow up
Need to complete the dose rate assessment for the DCLL TBM
Comments
With the recent advances in computers soft and hardware development, the limitation on disk space requirement is much more relaxed.
Discrete ordinates codes (e.g. ATTILA/SEVERIAN)are good tools for engineering designs that require frequent design modifications.
ATTILA is already extensively used in ITER in-vessel component designs (diagnostics, ELM.VS, etc.)

27. Features Comparison of Recently Developed Discrete Ordinates Codes - 1/4

28. Features Comparison of Recently Developed Discrete Ordinates Codes - 2/4

29. Features Comparison of Recently Developed Discrete Ordinates Codes - 3/4

30. Features Comparison of Recently Developed Discrete Ordinates Codes - 4/4