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Numerical Stability of Existing Monte Carlo Burnup Codes in Cycle Calculations of Critical Reactors
KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.ORCID iD: 0000-0002-7943-7517
2009 (English)In: Nuclear science and engineering, ISSN 0029-5639, Vol. 162, no 3, 307-311 p.Article in journal (Refereed) Published
Abstract [en]

We show that major existing Monte Carlo burnup codes are numerically unstable in cycle calculations of critical reactors; spatial oscillations of the neutron flux can be observed even when relatively small time steps are used. This is caused by using the explicit Euler or midpoint method that appear to be numerically unstable with the step sizes common in cycle calculations. More stable methods that are common in deterministic burnup calculations, like the modified Euler method, can easily be introduced into the Monte Carlo burnup codes.

Place, publisher, year, edition, pages
2009. Vol. 162, no 3, 307-311 p.
Keyword [en]
Burn up; Burnup calculation; Critical reactors; Midpoint method; Modified Euler method; MONTE CARLO; Numerical stabilities; Spatial oscillations; Step size; Time step
National Category
Physical Sciences
URN: urn:nbn:se:kth:diva-14050ISI: 000267621400008ScopusID: 2-s2.0-68649086454OAI: diva2:329376
QC 20100709Available from: 2010-07-09 Created: 2010-07-09 Last updated: 2010-07-16Bibliographically approved
In thesis
1. Development of New Monte Carlo Methods in Reactor Physics: Criticality, Non-Linear Steady-State and Burnup Problems
Open this publication in new window or tab >>Development of New Monte Carlo Methods in Reactor Physics: Criticality, Non-Linear Steady-State and Burnup Problems
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The Monte Carlo method is, practically, the only approach capable of giving detail insight into complex neutron transport problems. In reactor physics, the method has been used mainly for determining the keff in criticality calculations. In the last decade, the continuously growing computer performance has allowed to apply the Monte Carlo method also on simple burnup simulations of nuclear systems. Nevertheless, due to its extensive computational demands the Monte Carlo method is still not used as commonly as deterministic methods.

One of the reasons for the large computational demands of Monte Carlo criticality calculations is the necessity to carry out a number of inactive cycles to converge the fission source. This thesis presents a new concept of fission matrix based Monte Carlo criticality calculations where inactive cycles are not required. It is shown that the fission matrix is not sensitive to the errors in the fission source, and can be thus calculated by a Monte Carlo calculation without inactive cycles. All required results, including keff, are then derived via the final fission matrix. The confidence interval for the estimated keff can be conservatively derived from the variance in the fission matrix. This was confirmed by numerical test calculations of Whitesides's ``keff of the world problem'' model where other Monte Carlo methods fail to estimate the confidence interval correctly unless a large number of inactive cycles is simulated.


Another problem is that the existing Monte Carlo criticality codes are not well shaped for parallel computations; they cannot fully utilise the processing power of modern multi-processor computers and computer clusters. This thesis presents a new parallel computing scheme for Monte Carlo criticality calculations based on the fission matrix. The fission matrix is combined over a number of independent parallel simulations, and the final results are derived by means of the fission matrix. This scheme allows for a practically ideal parallel scaling since no communication among the parallel simulations is required, and no inactive cycles need to be simulated.


When the Monte Carlo criticality calculations are sufficiently fast, they will be more commonly applied on complex reactor physics problems, like non-linear steady-state calculations and fuel cycle calculations. This thesis develops an efficient method that introduces thermal-hydraulic and other feedbacks into the numerical model of a power reactor, allowing to carry out a non-linear Monte Carlo analysis of the reactor with steady-state core conditions. The thesis also shows that the major existing Monte Carlo burnup codes use unstable algorithms for coupling the neutronic and burnup calculations; therefore, they cannot be used for fuel cycle calculations. Nevertheless, stable coupling algorithms are known and can be implemented into the future Monte Carlo burnup codes.


Place, publisher, year, edition, pages
Stockholm: Universitetsservice US AB, 2009. xi, 49 p.
Trita-FYS, ISSN 0280-316X ; 2009:20
Monte Carlo, reactor physics, fission source, inactive cycles, convergence, burnup, steady-state, criticality, eigenvalue
National Category
Subatomic Physics
urn:nbn:se:kth:diva-10602 (URN)978-91-7415-366-8 (ISBN)
Public defence
2009-06-11, Sal FA32, AlbaNova, Roslagstullsbacken 21, Stockholm, 13:15 (English)
QC 20100709Available from: 2009-06-04 Created: 2009-06-01 Last updated: 2010-07-16Bibliographically approved

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