A Two-Dimensional Time-Dependent Neutron Transport Calculation Using One-Dimensional Equations

1976 ◽  
Vol 61 (1) ◽  
pp. 117-118
Author(s):  
Michael Boring ◽  
W. H. Roach
Keyword(s):  
Neutron Transport ◽  
Time Dependent ◽  
Two Dimensional ◽  
One Dimensional ◽  
Transport Calculation

On the similarity of particle and photon tunneling and multiple internal reflections in one-dimensional, two-dimensional and three-dimensional photon tunneling

2014 ◽  
Vol 23 (06) ◽  
pp. 1460006 ◽  
Author(s):  
V. S. Olkhovsky
Keyword(s):  
Quantum Electrodynamics ◽  
Electromagnetic Waves ◽  
Relativistic Quantum ◽  
Three Dimensional ◽  
Time Dependent ◽  
Two Dimensional ◽  
Relativistic Quantum Field Theory ◽  
One Dimensional ◽  
Quantum Equation ◽  
Photon Tunneling

The formal mathematical analogy between time-dependent quantum equation for the nonrelativistic particles and time-dependent equation for the propagation of electromagnetic waves had been studied in [A. I. Akhiezer and V. B. Berestezki, Quantum Electrodynamics (FM, Moscow, 1959) [in Russian] and S. Schweber, An Introduction to Relativistic Quantum Field Theory, Chap. 5.3 (Row, Peterson & Co, Ill, 1961)]. Here, we deal with the time-dependent Schrödinger equation for nonrelativistic particles and with time-dependent Helmholtz equation for electromagnetic waves. Then, using this similarity, the tunneling and multiple internal reflections in one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) particle and photon tunneling are studied. Finally, some conclusions and future perspectives for further investigations are presented.

Development of a Two-Dimensional Modularity Characteristics Code for Neutron Transport Calculation

2013 ◽  
Author(s):  
Liang Liang ◽  
Hongchun Wu ◽  
Liangzhi Cao ◽  
Youqi Zheng
Keyword(s):  
Large Scale ◽  
Method Of Characteristics ◽  
Neutron Transport ◽  
Engineering Application ◽  
Polar Angle ◽  
Two Dimensional ◽  
Coarse Mesh ◽  
Characteristics Method ◽  
Large Scale Problems ◽  
Transport Calculation

The method of characteristics (MOC) has been widely used in lattice code for its high precision and easy complement. However, the long characteristics method needs large quantity of PC memory when dealing with large scale problems. The modularity MOC method could significantly reduce the PC memory when calculating the problem which contains lots of repeatedly geometries, like the fuel assembly in the reactor. In this method, only typical geometric cells are selected to trace the rays, and then the geometry information of these cells is stored. So, the modularity MOC method is feasible to perform well in the calculation with large scale. When tracing the rays, the technique of mesh ray generating and the corresponding azimuthal quadrature set are both applied. The techniques make sure that each ray has the reflected ray in the boundary so it is convenient to describe the boundary condition. The optimal polar angle and the Guass quadrature set are selected as the polar quadrature set. Furthermore, the coarse mesh finite difference (CMFD) is employed to accelerate the calculation. A pin cell is chosen as the coarse mesh. The CMFD solution provides the MOC with much faster converged fission and scattering source distributions. The LOTUS code is developed and the numerical results show that the code is precise for engineering application and the CMFD acceleration is effective.

scholarly journals Analytical solutions for the neutron transport using the spectral methods

2006 ◽  
Vol 2006 ◽  
pp. 1-11 ◽  
Author(s):  
Abdelouahab Kadem
Keyword(s):  
Analytical Solutions ◽  
Spectral Methods ◽  
Chebyshev Polynomials ◽  
Neutron Transport ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
One Dimensional ◽  
Multidimensional Problems ◽  
Dimensional Equation ◽  
Transport Problems

We present a method for solving the two-dimensional equation of transfer. The method can be extended easily to the general linear transport problem. The used technique allows us to reduce the two-dimensional equation to a system of one-dimensional equations. The idea of using the spectral method for searching for solutions to the multidimensional transport problems leads us to a solution for all values of the independant variables, the proposed method reduces the solution of the multidimensional problems into a set of one-dimensional ones that have well-established deterministic solutions. The procedure is based on the development of the angular flux in truncated series of Chebyshev polynomials which will permit us to transform the two-dimensional problem into a set of one-dimensional problems.

Two-dimensional time dependent Riemann solvers for neutron transport

2005 ◽  
Vol 210 (1) ◽  
pp. 386-399 ◽  
Author(s):  
Thomas A. Brunner ◽  
James Paul Holloway
Keyword(s):  
Neutron Transport ◽  
Time Dependent ◽  
Two Dimensional ◽  
Riemann Solvers

scholarly journals ANALYSIS OF TIME-EIGENVALUE AND EIGENFUNCTIONS IN THE CROCUS BENCHMARK

2021 ◽  
Vol 247 ◽  
pp. 04011
Author(s):  
Yasushi Nauchi ◽  
Alexis Jinaphanh ◽  
Andrea Zoia
Keyword(s):  
Neutron Emission ◽  
Neutron Transport ◽  
Fission Neutron ◽  
Time Dependent ◽  
Natural Mode ◽  
Probability Method ◽  
Dominant Eigenvalue ◽  
Transport Calculation ◽  
Fission Probability ◽  
Good Agreement

Time-dependent neutron transport in non-critical state can be expressed by the natural mode equation. In order to estimate the dominant eigenvalue and eigenfunction of the natural mode, CEA had extended the α-k method and developed the generalized iterated fission probability method (G-IFP) in the TRIPOLI-4® code. CRIEPI has chosen to compute those quantities by a time-dependent neutron transport calculation, and has thus developed a time-dependent neutron transport technique based on k-power iteration (TDPI) in MCNP-5. In this work, we compare the two approaches by computing the dominant eigenvalue and the direct and adjoint eigenfunctions for the CROCUS benchmark. The model has previously been qualified for keffs and kinetic parameters by TRIPOLI-4 and MCNP-5. The eigenvalues of the natural mode equations by α-k and TDPI are in good agreement with each other, and closely follow those predicted by the inhour equation. Neutron spectra and spatial distributions (flux and fission neutron emission) obtained by the two methods are also in good agreement. Similar results are also obtained for the adjoint fundamental eigenfunctions. These findings substantiate the coherence of both calculation strategies for natural mode.

scholarly journals GPU Based Two-Level CMFD Accelerating Two-Dimensional MOC Neutron Transport Calculation

2020 ◽  
Vol 8 ◽  
Author(s):  
Peitao Song ◽  
Qian Zhang ◽  
Liang Liang ◽  
Zhijian Zhang ◽  
Qiang Zhao
Keyword(s):  
Neutron Transport ◽  
Two Dimensional ◽  
Transport Calculation

Pattern formation on time-dependent domains

2019 ◽  
Vol 880 ◽  
pp. 136-179 ◽  
Author(s):  
M. Ghadiri ◽  
R. Krechetnikov
Keyword(s):  
Liquid Layer ◽  
Three Dimensional ◽  
Time History ◽  
Domain Size ◽  
Vertical Vibration ◽  
Time Dependent ◽  
Two Dimensional ◽  
Layer Depth ◽  
One Dimensional ◽  
Aspect Ratios

In the quest to understand the dynamics of distributed systems on time-dependent spatial domains, we study experimentally the response to domain deformations by Faraday wave patterns – standing waves formed on the free surface of a liquid layer due to its vertical vibration – chosen as a paradigm owing to their historical use in testing new theories and ideas. In our experimental set-up of a vibrating water container with controlled positions of lateral walls and liquid layer depth, the characteristics of the patterns are measured using the Fourier transform profilometry technique, which allows us to reconstruct an accurate time history of the pattern three-dimensional landscape and reveal how it reacts to the domain dynamics on various length and time scales. Analysis of Faraday waves on growing, shrinking and oscillating domains leads to a number of intriguing results. First, the observation of a transverse instability – namely, when a two-dimensional pattern experiences an instability in the direction orthogonal to the direction of the domain deformation – provides a new facet to the stability picture compared to the one-dimensional systems in which the longitudinal (Eckhaus) instability accounts for pattern transformation on time-varying domains. Second, the domain evolution rate is found to be a key factor dictating the patterns observed on the path between the initial and final domain aspect ratios. Its effects range from allowing the formation of complex sequences of patterns to impeding the appearance of any new pattern on the path. Third, the shrinkage–growth process turns out to be generally irreversible on a horizontally evolving domain, but becomes reversible in the case of a time-dependent liquid layer depth, i.e. when the dilution and convective effects of the domain flow are absent. These experimentally observed enigmatic effects of the domain size variations in time are complemented here with appropriate theoretical insights elucidating the dynamics of two-dimensional pattern evolution, which proves to be more intricate compared to one-dimensional systems.

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