Editing Neutron transport (section)

==Computational methods==
Both fixed-source and criticality calculations can be solved using [[Deterministic system (mathematics)|deterministic methods]] or [[stochastic process|stochastic methods]]. In deterministic methods the transport equation (or an approximation of it, such as [[Diffusion process|diffusion theory]]) is solved as a differential equation. In stochastic methods such as [[Monte Carlo method|Monte Carlo]] discrete particle histories are tracked and averaged in a random walk directed by measured interaction probabilities. Deterministic methods usually involve multi-group approaches while Monte Carlo can work with multi-group and continuous energy cross-section libraries. Multi-group calculations are usually iterative, because the group constants are calculated using flux-energy profiles, which are determined as the result of the neutron transport calculation.

===Discretization in deterministic methods===
To numerically solve the transport equation using algebraic equations on a computer, the spatial, angular, energy, and time variables must be [[Discretization|discretized]]. 
* Spatial variables are typically discretized by simply breaking the geometry into many small regions on a mesh. The balance can then be solved at each mesh point using [[finite difference]] or by nodal methods. 
* Angular variables can be discretized by discrete ordinates and weighting [[Numerical integration|quadrature sets]] (giving rise to the [[Discrete Ordinates Method|S<sub>N</sub> methods]]), or by functional expansion methods with the [[spherical harmonics]] (leading to the P<sub>N</sub> methods).
* Energy variables are typically discretized by the multi-group method, where each energy group represents one constant energy. As few as 2 groups can be sufficient for some [[Thermal-neutron reactor|thermal reactor]] problems, but [[Fast-neutron reactor|fast reactor]] calculations may require many more. 
* The time variable is broken into discrete time steps, with time derivatives replaced with difference formulas.

===Computer codes used in neutron transport===

====Probabilistic codes====
*''COG -'' A LLNL developed Monte Carlo code for criticality safety analysis and general radiation transport (<nowiki>http://cog.llnl.gov</nowiki>)
*''MCBEND'' <ref>{{cite web|title=MCBEND|url=https://www.answerssoftwareservice.com/mcbend/}}</ref> – A Monte Carlo code for general radiation transport developed and supported by the ANSWERS Software Service.<ref name="ANSWERS">{{cite web|title=ANSWERS|url=https://www.answerssoftwareservice.com/}}</ref>
*''[[MCNP]]'' – A [[Los Alamos National Laboratory|LANL]] developed Monte Carlo code for general radiation transport
*MC21<ref>{{Cite report |url=https://www.osti.gov/biblio/903083 |title=The MC21 Monte Carlo Transport Code |date=2007-01-09 |publisher=Knolls Atomic Power Lab. (KAPL), Niskayuna, NY (United States) |issue=LM-06K144 |osti=903083 |language=English}}</ref> – A general-purpose, 3D Monte Carlo code developed at [[Knolls Atomic Power Laboratory|NNL]].
*''MCS'' – The Monte Carlo code MCS has been developed since 2013 at Ulsan National Institute of Science and Technology (UNIST), Republic of Korea.<ref>{{cite web|title=MCS|url=http://reactorcore.unist.ac.kr/mcs/}}</ref>
*''Mercury'' – A [[Lawrence Livermore National Laboratory|LLNL]] developed Monte Carlo particle transport code.<ref>{{cite web|title=Mercury|url=https://wci.llnl.gov/simulation/computer-codes/mercury}}</ref>
*''MONK'' <ref>{{cite web|title=MONK|url=https://www.answerssoftwareservice.com/monk/}}</ref> – A Monte Carlo Code for criticality safety and reactor physics analyses developed and supported by the ANSWERS Software Service.<ref name="ANSWERS" /> 
*''MORET'' – Monte-Carlo code for the evaluation of criticality risk in nuclear installations developed at IRSN, France<ref>{{cite web|title=MORET5|url=https://www.irsn.fr/EN/Research/Scientific-tools/Computer-codes/Pages/Moret-Code.aspx}}</ref>
*''OpenMC'' – An open source, community-developed open source Monte Carlo code<ref>{{cite web|title=OpenMC|url=https://docs.openmc.org/}}</ref>
*''RMC'' – A [[Tsinghua University]] Department of Engineering Physics developed Monte Carlo code for general radiation transport
*SCONE – The '''S'''tochastic '''C'''alculator '''O'''f the '''N'''eutron Transport '''E'''quation, an open-source Monte Carlo code developed at the University of Cambridge.<ref>{{Cite web |title=SCONE |url=https://github.com/CambridgeNuclear/SCONE |website=[[GitHub]]}}</ref>
*''[[Serpent (software)|Serpent]]'' – A [[VTT Technical Research Centre of Finland]] developed Monte Carlo particle transport code<ref>{{cite web|title=Serpent – A Monte Carlo Reactor Physics Burnup Calculation Code|url=http://montecarlo.vtt.fi/|access-date=2013-12-03|archive-url=https://web.archive.org/web/20140901002129/http://montecarlo.vtt.fi/|archive-date=2014-09-01|url-status=dead}}</ref>
*''Shift/KENO'' – [[Oak Ridge National Laboratory|ORNL]] developed Monte Carlo codes for general radiation transport and criticality analysis
*''TRIPOLI'' – 3D general purpose continuous energy Monte Carlo Transport code developed at CEA, France<ref>{{cite web|title=TRIPOLI-4|date=19 October 2013|url=http://www.cea.fr/nucleaire/tripoli-4}}</ref>
*''UCN'' - Monte Carlo transport code for simulating experiments with ultracold neutrons developed at PNPI, Gatchina<ref>{{cite journal | last1=Fomin | first1=A.K. | last2=Serebrov | first2=A.P. | title=Monte Carlo Model of the Experiment on Measuring the Neutron Lifetime | journal=Mathematical Models and Computer Simulations | volume=10 | issue=6 | year=2018 | doi=10.1134/S2070048218060066 | pages=741–747}}</ref>

====Deterministic codes====
*''Ardra'' – A [[Lawrence Livermore National Laboratory|LLNL]] neutral particle transport code <ref>{{cite web|title=Ardra|url=https://computing.llnl.gov/projects/ardra-scaling-up-sweep-transport-algorithms}}</ref>
*''Attila'' – A commercial transport code
*''DRAGON'' – An open-source lattice physics code
*''PHOENIX/ANC'' – A proprietary lattice-physics and global diffusion code suite from [[Westinghouse Electric Corporation|Westinghouse Electric]]
*''PARTISN'' – A [[Los Alamos National Laboratory|LANL]] developed transport code based on the discrete ordinates method<ref>{{Cite web |title=RSICC CODE PACKAGE CCC 760 |url=https://rsicc.ornl.gov/codes/ccc/ccc8/ccc-842.html |access-date=2022-08-05 |website=rsicc.ornl.gov}}</ref>
*''NEWT'' – An [[Oak Ridge National Laboratory|ORNL]] developed 2-D S<sub>N</sub> code <ref name=":0">{{Cite web |title=SCALE Overview {{!}} ORNL |url=https://www.ornl.gov/scale/overview |access-date=2022-08-05 |website=www.ornl.gov}}</ref>
*''DIF3D/VARIANT'' – An Argonne National Laboratory developed 3-D code originally developed for fast reactors <ref>{{Cite web |title=Software: DIF3D – Nuclear Engineering Division (Argonne) |url=https://www.ne.anl.gov/codes/dif3d/ |access-date=2022-08-05 |website=www.ne.anl.gov}}</ref>
*''DENOVO'' – A massively parallel transport code under development by [[Oak Ridge National Laboratory|ORNL]]<ref name=":0" /><ref>{{Cite journal |last1=Evans |first1=Thomas M. |last2=Stafford |first2=Alissa S. |last3=Slaybaugh |first3=Rachel N. |last4=Clarno |first4=Kevin T. |date=2010-08-01 |title=Denovo: A New Three-Dimensional Parallel Discrete Ordinates Code in SCALE |url=https://doi.org/10.13182/NT171-171 |journal=Nuclear Technology |volume=171 |issue=2 |pages=171–200 |doi=10.13182/NT171-171 |bibcode=2010NucTe.171..171E |s2cid=93751324 |issn=0029-5450|url-access=subscription }}</ref>
*''Jaguar'' – A parallel 3-D [[Slice Balance Approach]] transport code for arbitrary polytope grids developed at [[Knolls Atomic Power Laboratory|NNL]]<ref>{{cite book |last1=Watson |first1=A. M. |last2=Grove |first2=R. E. |last3=Shearer |first3=M. T. |title=Effective software design for a deterministic transport system |date=2009 |publisher=American Nuclear Society |isbn=978-0-89448-069-0 |url=https://inis.iaea.org/search/searchsinglerecord.aspx?recordsFor=SingleRecord&RN=42064864 |access-date=5 August 2022}}</ref>
*''DANTSYS''
*''RAMA'' – A proprietary 3D [[method of characteristics]] code with arbitrary geometry modeling, developed for [[Electric Power Research Institute|EPRI]] by TransWare Enterprises Inc.<ref>{{cite web|title=RAMA|url=http://adamswebsearch2.nrc.gov/webSearch2/main.jsp?AccessionNumber=ML050750478}}</ref>
*''RAPTOR-M3G'' – A proprietary parallel radiation transport code developed by [[Westinghouse Electric Company]]
*''OpenMOC'' – An [[Massachusetts Institute of Technology|MIT]] developed open source parallel [[method of characteristics]] code<ref>{{cite web|title=OpenMOC|url=https://mit-crpg.github.io/OpenMOC/}}</ref>
*''MPACT'' – A parallel 3D [[method of characteristics]] code under development by [[Oak Ridge National Laboratory]] and the [[University of Michigan]]
*''DORT'' – Discrete Ordinates Transport
*''APOLLO'' – A lattice physics code used by [[French Alternative Energies and Atomic Energy Commission|CEA]], [[Électricité de France|EDF]] and [[Areva NC|Areva]]<ref>{{cite web|title=APOLLO3|url=http://mathematicsandcomputation.cowhosting.net/MC09/pdfs/201216.pdf|access-date=2015-08-29|archive-url=https://web.archive.org/web/20151222075936/http://mathematicsandcomputation.cowhosting.net/MC09/pdfs/201216.pdf|archive-date=2015-12-22|url-status=dead}}</ref>
*''CASMO/SIMULATE'' – A proprietary lattice-physics and diffusion code suite developed by [[Studsvik]] for [[Light-water reactor|LWR]] analysis including square and hex lattices<ref>{{cite web|title=CASMO5|url=https://www.studsvik.com/testing-new-web/start2/testing-new-web2/start/business/products/casmo/
}}</ref>
*''HELIOS'' – A proprietary lattice-physics code with generalized geometry developed by [[Studsvik]] for [[Light-water reactor|LWR]] analysis<ref>{{cite web|title=CASMO5|url=https://www.studsvik.com/testing-new-web/start2/testing-new-web2/start/business/products/helios/
}}</ref>
*''milonga'' – A free nuclear reactor core analysis code<ref>{{cite web|title=Milonga|url=https://www.seamplex.com/milonga}}</ref>
*''STREAM'' –  A neutron transport analysis code, STREAM (Steady state and Transient REactor Analysis code with Method of Characteristics), has been developed since 2013 at Ulsan National Institute of Science and Technology (UNIST), Republic of Korea <ref>{{cite web|title=STREAM|url=http://reactorcore.unist.ac.kr/stream/}}</ref>