1 ufttg nuclear & radiological engineering particle transport methods in parallel environments...

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Nuclear & Radiological Engineering

Particle Transport Methods in Particle Transport Methods in Parallel Environments Parallel Environments

Prof. A. Haghighat ([email protected])Prof. A. Haghighat ([email protected])

Nuclear & Radiological Engineering DepartmentNuclear & Radiological Engineering Department

University of FloridaUniversity of Florida202 Nuclear Sciences Building202 Nuclear Sciences Building

Gainesville, FL 32611, USAGainesville, FL 32611, USA

[Prepared for a meeting with Dell/HPC visitors, Dec. 13, 2002][Prepared for a meeting with Dell/HPC visitors, Dec. 13, 2002]

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Objective

Simulation of particle transport of real-life nuclear systems (power reactors, medical devices, detection devices) for design and optimization

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Particle Transport Theory

Expected number of particles in a phase space (dVdEd) at time t:

z

x

y

Ω

r

dv

dΩ

n(r, E, Ω, t) dVdEd

dE

Definitions

Angular flux - Scalar flux -

Reaction rate density = macroscopic cross-section

),ˆ,,()(),ˆ,,( tErnEvtEr ),ˆ,,(),,(

4

tErdtEr

),,(),( tErEr ),( Er

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Particle Transport Theory Approaches

Deterministic

Statistical Monte Carlo

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Deterministic Transport Theory Approach

• Linear Boltzmann equation (steady-state)

Balance equation for expected number of particles in a phase space (dVdEd);

)ˆ,,()ˆ,',(),(''4

)(

)ˆ,',()ˆ'ˆ,',(''

)ˆ,,(),()ˆ,,(.ˆ

0 4

0 4

ErSErErddEE

ErEErddE

ErErEr

f

s

Streaming Collision

Scattering

FissionIndependent source

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Sn Method• The Sn balance equation for a spatial grid, group g, direction m is

given by

Amg

Amgg

Bmg

Tmg

mRmg

Lmg

mInmg

Outmg

m qzyx ,,,,,,,, )()()(

where

There are 6 independent variables, e.g., x,y,z, E, and

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Issues

•Need for large computer memory, e.g., for a typical shielding problem with

100x100x100 (space) x 80 (directions)x 50 (groups)

memory required = 32 GB !

•Need for significant computation time because of slow convergence

PENTRANPENTRANTMTM (Parallel Environment Neutral-particle TRANsport)(Parallel Environment Neutral-particle TRANsport) and its applicationand its application

to Real-Life Nuclear Systemsto Real-Life Nuclear Systems

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PENTRANPENTRANTM TM (1) (1)

Parallel Environment Neutral-particle TRANsport developed from scratch in 1996:– ANSI FORTRAN F77/f90 with MPI library, over 33,000 lines – Industry standard FIDO input

Solves 3-D Cartesian, multigroup, anisotropic transport problems – Forward and adjoint mode

– Fixed source, criticality eigenvalue problems

Parallel processing algorithms– Full phase-space decomposition: Parallel in angle, energy, and

spatial variables

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PENTRANPENTRANTMTM (2) (2)

(continued)– Parallel I/O – Partitioned memory for memory intensive arrays (angular

fluxes, etc)– Builds MPI processor communicators – Automatic scheduling using a decomposition weighting

vector

Numerical formulations– Adaptive Differencing Strategy

• Diamond Zero (DZ)• Directional Theta-Weighted differencing (DTW)• Exponential-Directional Weighted (EDW)

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(continue)– Allows for a fully discontinuous variable meshing

between coarse meshes: Uses a novel higher order mesh coupling scheme: Taylor Projection Mesh Coupling (TPMC)

– Acceleration• Spatial Two-grid (“/”) with TPMC • Angular multigrid (AMG) formulations with TPMC• PCR with a zoned rebalance acceleration• AMG + PCR

– Iterative techniques• Multigroup & One-level SI schemes

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– Red-Black and Block Jacobi iteration– Anisotropic scattering via Legendre moments through P7,– Angular quadrature set:

• Level symmetric (up to S20) with ordinate splitting (OS)

• Pn-Tn with OS

– Vacuum, reflective, and albedo boundaries – Volumetric & planar angular sources

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PENTRAN Performance

Achieved high parallel fractions of 90-98% for solving real-life problems such as

a BWR core shroud; a PWR cavity dosimetry;

CT scan; X-ray room

Compared well with theoretical predictions

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Monte Carlo Methods

Simulation of a physical process on a computer by sampling PDFs of basic physical processes using Random Numbers

Issues

Large computation time

Achieving small variance

Solution

Parallel Monte Carlo (it is straightforward; embarrassingly parallel)

Variance reduction methods (developed automated adjoint-based algorithms)

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Activities/interests

Parallel computing

PTDC laboratory at NRE contains 2 PC clusters:

•8 machines with 2 GB memory dedicated to LBE

•6 machines with 1 GB memory dedicated to Monte Carlo

Web-based Computing

PENTRAN code system is available on the web

High Performance Computing graduate minor/certificate

We are preparing a proposal

1 ufttg nuclear & radiological engineering particle transport methods in parallel environments...

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