Neutron Transport in Moving Media

Kinetic theory is the branch of statistical physics dealing with the dynamics of non-equilibrium processes and their relaxation to thermodynamic equilibrium. Established by Ludwig Boltzmann (1844–1906) in 1872, his eponymous equation stands as its mathematical cornerstone. Originally developed in the framework of dilute gas systems, the Boltzmann equation has spread its wings across many areas of modern statistical physics, including electron transport in semiconductors, neutron transport, quantum-relativistic fluids in condensed matter and even subnuclear plasmas. In this Chapter, a basic introduction to the Boltzmann equation in the context of classical statistical mechanics shall be provided.

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Convergence analysis of the non-linear CMFD schemes for acceleration of multi-group fixed source neutron transport calculations

Annals of Nuclear Energy ◽

10.1016/j.anucene.2020.108041 ◽

2021 ◽

Vol 153 ◽

pp. 108041

Author(s):

Lakshay Jain ◽

Mohanakrishnan Prabhakaran ◽

Ramamoorthy Karthikeyan ◽

Umasankari Kannan

Keyword(s):

Convergence Analysis ◽

Neutron Transport ◽

Source Neutron ◽

Non Linear

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Benchmarking GEANT4 and PHITS for 14.8-MeV neutron transport in polyethylene and graphite materials

Fusion Engineering and Design ◽

10.1016/j.fusengdes.2021.112720 ◽

2021 ◽

pp. 112720

Author(s):

Xin Zhang ◽

Zhiqiang Chen ◽

Rui Han ◽

Guoyu Tian ◽

Bingyan Liu ◽

...

Keyword(s):

Neutron Transport

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A Revisit to CMFD Schemes: Fourier Analysis and Enhancement

Energies ◽

10.3390/en14020424 ◽

2021 ◽

Vol 14 (2) ◽

pp. 424

Author(s):

Dean Wang ◽

Zuolong Zhu

Keyword(s):

Fourier Analysis ◽

Eigenvalue Problems ◽

Neutron Transport ◽

Coarse Mesh ◽

Successive Overrelaxation ◽

Computational Cell ◽

Artificial Diffusion ◽

Acceleration Method ◽

The Stability ◽

Partial Current

The coarse-mesh finite difference (CMFD) scheme is a very effective nonlinear diffusion acceleration method for neutron transport calculations. CMFD can become unstable and fail to converge when the computational cell optical thickness is relatively large in k-eigenvalue problems or diffusive fixed-source problems. Some variants and fixups have been developed to enhance the stability of CMFD, including the partial current-based CMFD (pCMFD), optimally diffusive CMFD (odCMFD), and linear prolongation-based CMFD (lpCMFD). Linearized Fourier analysis has proven to be a very reliable and accurate tool to investigate the convergence rate and stability of such coupled high-order transport/low-order diffusion iterative schemes. It is shown in this paper that the use of different transport solvers in Fourier analysis may have some potential implications on the development of stabilizing techniques, which is exemplified by the odCMFD scheme. A modification to the artificial diffusion coefficients of odCMFD is proposed to improve its stability. In addition, two explicit expressions are presented to calculate local optimal successive overrelaxation (SOR) factors for lpCMFD to further enhance its acceleration performance for fixed-source problems and k-eigenvalue problems, respectively.

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