Analytical three-dimensional neutron transport benchmarks for verification of nuclear engineering codes. Final report

Ganapol, B. D.; Kornreich, Drew E.

doi:10.2172/505359

Cited by 8 publications

(13 citation statements)

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“…This verification is necessary before the results of MC simulations can be considered a gold standard in transport phenomena 2 , 3 , 29 . More in general, a MC code (as any other code that “solves” integro-differential equations) should go through verification and validation procedures 30 , 31 . By the term “verification” is meant a series of procedures to ascertain that a code is computationally sound, in other words that it carries out the calculations it is supposed to, without any bugs 30 , 31 .…”

Section: Introductionmentioning

confidence: 99%

“…More in general, a MC code (as any other code that “solves” integro-differential equations) should go through verification and validation procedures 30 , 31 . By the term “verification” is meant a series of procedures to ascertain that a code is computationally sound, in other words that it carries out the calculations it is supposed to, without any bugs 30 , 31 . While for “validation” is meant the comparison between the numerical results generated by a code with experimental results from a physical system that the code is supposed to model 30 , 32 .…”

Section: Introductionmentioning

confidence: 99%

“…By the term “verification” is meant a series of procedures to ascertain that a code is computationally sound, in other words that it carries out the calculations it is supposed to, without any bugs 30 , 31 . While for “validation” is meant the comparison between the numerical results generated by a code with experimental results from a physical system that the code is supposed to model 30 , 32 . In this work, we propose a verification method for MC codes devised for “solving” the transport equation.…”

Section: Introductionmentioning

confidence: 99%

“…This work proposes a verification procedure of Monte Carlo codes that is a contribution to fill this gap. The proposed method, compared to previous used semi-analytical benchmarks 30 , 45 – 48 , is able to test the correctness of MC codes in more complex geometries and/or distribution of the optical properties. The procedure is capable of detecting various types of errors in a MC code and is particularly sensible to inaccuracies in the treatment of boundaries.…”

Section: Introductionmentioning

confidence: 99%

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Verification method of Monte Carlo codes for transport processes with arbitrary accuracy

Martelli

Tommasi

Sassaroli

et al. 2021

Sci Rep

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In this work, we present a robust and powerful method for the verification, with arbitrary accuracy, of Monte Carlo codes for simulating random walks in complex media. Such random walks are typical of photon propagation in turbid media, scattering of particles, i.e., neutrons in a nuclear reactor or animal/humans’ migration. Among the numerous applications, Monte Carlo method is also considered a gold standard for numerically “solving” the scalar radiative transport equation even in complex geometries and distributions of the optical properties. In this work, we apply the verification method to a Monte Carlo code which is a forward problem solver extensively used for typical applications in the field of tissue optics. The method is based on the well-known law of average path length invariance when the entrance of the entities/particles in a medium obeys to a simple cosine law, i.e., Lambertian entrance, and annihilation of particles inside the medium is absent. By using this law we achieve two important points: (1) the invariance of the average path length guarantees that the expected value is known regardless of the complexity of the medium; (2) the accuracy of a Monte Carlo code can be assessed by simple statistical tests. We will show that we can reach an arbitrary accuracy of the estimated average pathlength as the number of simulated trajectories increases. The method can be applied in complete generality versus the scattering and geometrical properties of the medium, as well as in presence of refractive index mismatches in the optical case. In particular, this verification method is reliable to detect inaccuracies in the treatment of boundaries of finite media. The results presented in this paper, obtained by a standard computer machine, show a verification of our Monte Carlo code up to the sixth decimal digit. We discuss how this method can provide a fundamental tool for the verification of Monte Carlo codes in the geometry of interest, without resorting to simpler geometries and uniform distribution of the scattering properties.

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