Energy Group Treatments for Monte Carlo Neutron Transport - - PowerPoint PPT Presentation

Introduction Domain Decomposition High-Order/Low-Order Iteration Summary

Energy Group Treatments for Monte Carlo Neutron Transport Simulations

Nick Horelik

22.107 Project

May 17, 2012

Nick Horelik Energy Monte Carlo

Introduction Domain Decomposition High-Order/Low-Order Iteration Summary

1

Introduction Monte Carlo

2

Domain Decomposition Space Energy Analysis of Approach

3

High-Order/Low-Order Iteration CMFD Precedent Extension to Energy Analysis of Approach

4

Summary

Nick Horelik Energy Monte Carlo

Introduction Domain Decomposition High-Order/Low-Order Iteration Summary Monte Carlo

Introduction

Linear Time-independent Transport Equation

Nick Horelik Energy Monte Carlo

Introduction Domain Decomposition High-Order/Low-Order Iteration Summary Monte Carlo

Tally fluxes and reaction rates

φ =

1 WV

• j

wj ΣT (Ej)

Embarrasingly parallel Memory intense for large problems

Nick Horelik Energy Monte Carlo

Introduction Domain Decomposition High-Order/Low-Order Iteration Summary Space Energy Analysis of Approach

Domain Decomposition

Over 100 billion histories required for 1% statistics in each depletion region Many 10s of GBytes required per processor for the large number of tallies needed We need to split the problem up to have any hope

Nick Horelik Energy Monte Carlo

Introduction Domain Decomposition High-Order/Low-Order Iteration Summary Space Energy Analysis of Approach

Space

Distribute the spatial domain among different compute nodes Follow particles from birth to death, communicating information (weight, energy, direction, etc) to the appropriate node when it hits a boundary All compute nodes need access to entire energy spectrum of cross-section data for all isotopes space energy

Nick Horelik Energy Monte Carlo

Introduction Domain Decomposition High-Order/Low-Order Iteration Summary Space Energy Analysis of Approach

Energy

Current Approach

Split up the domain in energy instead of space Track particles through the entire geometry until they hit an energy boundary Conserving total weight, run different numbers of particles in each energy group

Focus computing power where it is harder to converge

space energy

Nick Horelik Energy Monte Carlo

Introduction Domain Decomposition High-Order/Low-Order Iteration Summary Space Energy Analysis of Approach

Analysis of Approach

Method

Batches of Particles Energy

Batch 1 start Nick Horelik Energy Monte Carlo

Introduction Domain Decomposition High-Order/Low-Order Iteration Summary Space Energy Analysis of Approach

Analysis of Approach

Method

Batches of Particles Energy

Batch 2 start Nick Horelik Energy Monte Carlo

Introduction Domain Decomposition High-Order/Low-Order Iteration Summary Space Energy Analysis of Approach

Analysis of Approach

Method

Batches of Particles Energy

Batch 3 start Nick Horelik Energy Monte Carlo

Introduction Domain Decomposition High-Order/Low-Order Iteration Summary Space Energy Analysis of Approach

Analysis of Approach

Method

Batches of Particles Energy

Batch 4 start Nick Horelik Energy Monte Carlo

Introduction Domain Decomposition High-Order/Low-Order Iteration Summary Space Energy Analysis of Approach

Analysis of Approach

Method

Batches of Particles Energy

Batch 1 done Nick Horelik Energy Monte Carlo

Introduction Domain Decomposition High-Order/Low-Order Iteration Summary Space Energy Analysis of Approach

Analysis of Approach

Method

Need to run more batches of particles than active tally batches

Problem dependent (how scattering)

Must conserve weight of all scatter sites for consistency

In each group g − → g ′ For each unfinished batch

Tallies need to be tracked until the active batch finishes

Significantly increases memory requirements

This is a book-keeping nightmare!

Nick Horelik Energy Monte Carlo

Introduction Domain Decomposition High-Order/Low-Order Iteration Summary Space Energy Analysis of Approach

At least it gives the expected results...

Nick Horelik Energy Monte Carlo

Introduction Domain Decomposition High-Order/Low-Order Iteration Summary Space Energy Analysis of Approach

Cost/Benefit

Fission site sampling requires more communications now, to start particles in the proper groups

Inhibits scaling – before fission sites could stay on the same compute node for the next batch

At worst all particles scatter out of the group to all other groups

For space, at worst they all scatter out to only the adjacent compute nodes

Cutting up the energy domain reduces cross section memory requirements for each node

However, more groups compounds the communications burden, and keeps batches alive longer (more tally memory needed)

As implemented, this hurts more than it helps

Nick Horelik Energy Monte Carlo

Introduction Domain Decomposition High-Order/Low-Order Iteration Summary CMFD Precedent Extension to Energy Analysis of Approach

High-Order/Low-Order Iteration

Perhaps we can find a way to separate batches from one another and not have to communicate as many sites between compute nodes Use Monte Carlo (high-order) as a fixed source solver in each group Use Diffusion (low-order) to set weights and ensure consistency of global tallies

Nick Horelik Energy Monte Carlo

Introduction Domain Decomposition High-Order/Low-Order Iteration Summary CMFD Precedent Extension to Energy Analysis of Approach

CMFD Precedent

Tally 1-group cross-sections and solve the spatial coarse mesh finite difference equations Update the weights of the next batch’s fission particles based

• n results

Speeds up Monte Carlo convergence for large problems that don’t interact much across large spatial distances

Hopefully we can acheive similar convergence acceleration

However this method is still fundamentally different, beacause we bank scatter sites

Nick Horelik Energy Monte Carlo

Introduction Domain Decomposition High-Order/Low-Order Iteration Summary CMFD Precedent Extension to Energy Analysis of Approach

Extension to Energy

Initially fully cover the energy spectrum Bank fission and scatter sites, noting g − → g′ Tally group and group-to-group cross sections for diffusion Use the diffusion solution to start the series of fixed source MC runs

Run full MC Tally group XSs & particle sites Solve multigroup diffusion Run fixed source MC Nick Horelik Energy Monte Carlo

Introduction Domain Decomposition High-Order/Low-Order Iteration Summary CMFD Precedent Extension to Energy Analysis of Approach

Only scatter site sampling, no diffusion weighting

Nick Horelik Energy Monte Carlo

Introduction Domain Decomposition High-Order/Low-Order Iteration Summary CMFD Precedent Extension to Energy Analysis of Approach

Only diffusion weighting

Nick Horelik Energy Monte Carlo

Introduction Domain Decomposition High-Order/Low-Order Iteration Summary CMFD Precedent Extension to Energy Analysis of Approach

Diffusion weighting & collision scaling

Nick Horelik Energy Monte Carlo

Introduction Domain Decomposition High-Order/Low-Order Iteration Summary

Summary

Brute-force energy domain decomposition doesn’t appear feasible, at least as implented here Deterministic acceleration in energy looks promising

Still much work to be done, different avenues to explore

Re-do the detailed Monte Carlo run periodically? Keep running update of tallied group cross sections?

Nick Horelik Energy Monte Carlo

Introduction Domain Decomposition High-Order/Low-Order Iteration Summary

Thank You

Questions?

Nick Horelik Energy Monte Carlo