```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
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
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
Deterministic Method:
Linear Boltzmann Transport Equation (LBTE)

ˆ
     t  Qscat  Qext
streaming collision
where,
sources



ˆ  r, E   E , 
ˆ 
ˆ 
Q scat   dE   d
s
0
4
• Represents a particle balance over a differential control
volume:
– Streaming + Collision = Scattering Source + Fixed
Source
– No particles lost
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
0.5 cm Element Size
Ωi
SN=Quadrature set of order N Number of angles in level-symmetric set= N(N+2)
Abdou Lecture 5
Scattering Source Expansion
• Scattering cross section is represented by expansion in Legendre
Polynomials


ˆ 
ˆ   2  r, E  E P  
 s r , E  E, 
s ,

0
 0 4


• The angular flux appearing in the scattering source is expanded in Spherical
Harmonics




 
 ˆ

ˆ
 r,
, E   m r , EYm 
 0 m   
Flux moments
Spherical Harmonics
• The degree of the expansion of the resulting scattering source is referred to
as the PN expansion order
scat
g
Q
Abdou Lecture 5
 
 
L

G
 ˆ

ˆ
r ,      s ,l , g  g r m, g Ym 
 0 m    g 1
PN=Harmonics
expansion
approximation 
number of
moments=(N+1)2
Energy Discretization
• Division of energy range into discrete groups (Muti-groups):

G
0
g 1
 dE  
• Multigroup constants are obtained by flux weighting, such as

 t , g r  

E g 1
Eg


 t , g r , E  r , E  dE

E g 1
Eg

 r , E  dE

• This is exact if  r , E  is known a priori



r
, E
• Highly accurate solutions can be obtained with approximations for
by a spectral weighting function
Spatial Discretization
•
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
•
unstrctured tetrahedral cells (3D)
– Cell sized can be controlled at preselected 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
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 5.23 x 1014
unknown
In unstructured tetrahedral grid
NT= ~5 x 1012 ( 2 orders of magnidude less)
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
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)
(PATISN)
- Linear discontinuous Galerkin finite element
- Trilinear-discontinuous Galerkin finite element
- Exponential discontinuous finite element
- Step characteristics, slice balance
(Denovo, PRTISN)
(Denovo)
(PARTISN)
(Denovo)
Arbitrary and Unstructured:
- Tri-linear discontinuous Finite Element (DFEM) on an arbitrary tetrahedral
mesh
(ATTILA)
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
-Transport synthetic acceleration (TSA)
(All)
(All)
Denovo: Parallel 3-D Discrete
Ordinates Code
 Denovo serves as the deterministic solver module in
the SCALE MAVRIC sequence
SCALE
Sn- 3-D Code
Denovo
Geom.
Model
Importance Sampling

.Developed
Appropriate
Weight windows
MAVRIC
Monaco with Automated Variance
Reduction using Importance
Mapping- Monte Carlo Code
to replace TORT as the principal 3-D
deterministic transport code for nuclear technology
applications at Oak Ridge National Laboratory (ORNL).
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
Over 1 Billion mesh
Slightly more
than 1 hr
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
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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
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
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
 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
Neutron Flux in the Vacuum Vessel
Looking down: Horizontal cut
at Mid-plane
Bottom of VV
Gamma Heating
Neutron Heating
W/cc
Total Heating is dominated by gamma heating
Accumulated Dose (Gy) in the Epoxy Insulator at 0.3 MW.a/m2
Gy
Diagnostics and Port shield Installed
2.01E6
1.92E6
PF4
1.67E6
PF4
1.58E6
9.02E4
Magnet
Insulator
PF5
PF6
1.16E5
4.48E4
PF5
PF6
3E3
3.67E4
2.11E5
5.27E4
Diagnostics/shield
not installed
•Dose in PF5 reduced by a factor of
100 when divertor port is plugged
Local Insulator Dose: The dose limit to the insulation is 10MGy
•Dose limit of 10 MGy is not reached
Dose (Gy/s) = Heating (W/cc)*1/ρmaterial*1000g/kg
Local Lifetime Limit 10 MGy, Assume Titer_life = 1.7E7 seconds
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
We have a meashable ITER
model with DCLL TBM inserted
Need to complete the dose rate assessment for the
DCLL TBM
• 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.)
Features Comparison of Recently Developed Discrete Ordinates Codes - 1/4
Features Comparison of Recently Developed Discrete Ordinates Codes - 2/4
Features Comparison of Recently Developed Discrete Ordinates Codes - 3/4
Features Comparison of Recently Developed Discrete Ordinates Codes - 4/4
```