ENTRANS: A platform for finite elements modeling of 3D neutron transport equation, Part II. Multidimensional implementation

2017 ◽  
Vol 101 ◽  
pp. 534-551 ◽  
Author(s):  
Mostafa Yousefi ◽  
A. Zolfaghari ◽  
A. Minuchehr ◽  
M.R. Abbassi
Keyword(s):  
Finite Elements ◽  
Transport Equation ◽  
Neutron Transport ◽  
Neutron Transport Equation ◽  
Finite Elements Modeling

scholarly journals HIGH-ORDER FINITE ELEMENTS FOR THE NEUTRON TRANSPORT EQUATION ON HONEYCOMB MESHES

2021 ◽  
Vol 247 ◽  
pp. 03002
Author(s):  
Ansar Calloo ◽  
Romain Le Tellier ◽  
David Labeurthre
Keyword(s):  
Finite Elements ◽  
Transport Equation ◽  
Neutron Transport ◽  
Computational Cost ◽  
Rational Functions ◽  
High Order ◽  
Severe Accident ◽  
Honeycomb Lattice ◽  
Spatial Problem ◽  
Neutron Transport Equation

Presently, APOLLO3®/MINARETsolves the transport equation using the multigroup Sn method with discontinuous finite elements on triangular meshes with Lagrange polynomial bases. The goal of this work is to solve the spatial problem on hexagonal geometries in the context of honeycomb lattice reactors, without further refining the computational mesh. The idea here is to construct high-order basis functions on the hexagonal element in order to improve the trade-off between computational cost and accuracy, in particular for multiphysics simulations where, often, thermalhydraulic modelling requires only assembly-average cross-sections to be defined (e.g.severe accident of fast breeder reactors)i.e.the assemblies are assumed homogeneous. One approach to achieve this goal is through the use of generalised barycentric functions such as the Wachspress rational functions. This research endeavour deals with the application of Wachspress rational functions to the neutron transport equation for hexagonal geometries up to order 3. With this method, it is possible to decrease the number of spatial unknowns required for the same accuracy, and thus the computational burden for complex geometries, such as honeycomb lattices is reduced.

High-Dimensional Model Representations for the Neutron Transport Equation

2014 ◽  
Vol 177 (3) ◽  
pp. 350-360 ◽  
Author(s):  
Zhengzheng Hu ◽  
Ralph C. Smith ◽  
Jeffrey Willert ◽  
C. T. Kelley
Keyword(s):  
Transport Equation ◽  
Neutron Transport ◽  
High Dimensional ◽  
Dimensional Model ◽  
Neutron Transport Equation
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