Calculation of λ modes of the multi-group neutron transport equation using the discrete ordinates and Finite Difference Method

2020 ◽  
Vol 137 ◽  
pp. 107077 ◽  
Author(s):  
S. Morató ◽  
Á. Bernal ◽  
R. Miró ◽  
Jose E. Roman ◽  
G. Verdú
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Transport Equation ◽  
Difference Method ◽  
Neutron Transport ◽  
Discrete Ordinates ◽  
Neutron Transport Equation

scholarly journals Intuitionistic fuzzy transport equation

2021 ◽  
Vol 27 (3) ◽  
pp. 83-97
Author(s):  
Zineb Belhallaj ◽  
◽  
Said Melliani ◽  
M'hamed Elomari ◽  
Lalla Saadia Chadli ◽  
...  
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Transport Equation ◽  
Difference Method ◽  
Advection Equation ◽  
Initial Condition ◽  
Generalized Differentiability ◽  
Intuitionistic Fuzzy ◽  
The Finite Difference Method

In the present paper, we use the generalized differentiability concept to study the intuitionistic fuzzy transport equation. We consider transport equation in the homogeneous and non-homogeneous cases with intuitionistic fuzzy initial condition. To illustrate the results, we will solve an advection equation using the finite difference method.

scholarly journals MULTILEVEL CMFD ACCELERATION METHODS FOR WHOLE CORE REACTOR SIMULATION IN VERA

2021 ◽  
Vol 247 ◽  
pp. 02037
Author(s):  
Luke Cornejo ◽  
Benjamin Collins ◽  
Shane Stimpson
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Virtual Environment ◽  
Difference Method ◽  
Neutron Transport ◽  
Coarse Mesh ◽  
Reactor Physics ◽  
Acceleration Methods ◽  
Solver Performance ◽  
Full Core

Ongoing efforts are being made to improve the performance of MPACT as the deterministic neutron transport solver in the Virtual Environment for Reactor Analysis (VERA). As other parts of the code have been improved, the coarse mesh finite difference method (CMFD) has come to take up a significant portion of the runtime. Multilevel-in-energy CMFD and multilevel-in-space CMFD solvers have been used to improve CMFD solver performance. A new multilevel-in-space-and-energy CMFD solver is being introduced that combines components of these two methods. W-Cycles and partial W-Cycles are being investigated to further improve the efficiency of the multilevel-in-energy CMFD solver. The performance of these methods is demonstrated on full core reactor physics problems of interest to VERA.

THE DISCRETE ORDINATES METHOD FOR THE NEUTRON TRANSPORT EQUATION IN AN INFINITE CYLINDRICAL DOMAIN

1992 ◽  
Vol 02 (03) ◽  
pp. 317-338 ◽  
Author(s):  
MOHAMMAD ASADZADEH ◽  
PETER KUMLIN ◽  
STIG LARSSON
Keyword(s):  
Transport Equation ◽  
Neutron Transport ◽  
Regularity Result ◽  
Discrete Ordinates ◽  
Cylindrical Domain ◽  
Neutron Transport Equation ◽  
Scalar Flux ◽  
Weakly Singular Kernel ◽  
Discrete Ordinates Method ◽  
Weakly Singular

We prove a regularity result for a Fredholm integral equation with weakly singular kernel, arising in connection with the neutron transport equation in an infinite cylindrical domain. The theorem states that the solution has almost two derivatives in L1, and is proved using Besov space techniques. This result is applied in the error analysis of the discrete ordinates method for the numerical solution of the neutron transport equation. We derive an error estimate in the L1-norm for the scalar flux, and as a consequence, we obtain an error bound for the critical eigenvalue.

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