scholarly journals High-Order Boundary Condition Perturbation Theory for the Neutron Transport Equation

2001 ◽  
Author(s):  
M S McKinley ◽  
F Rahnema
Keyword(s):  
Boundary Condition ◽  
Perturbation Theory ◽  
Transport Equation ◽  
Neutron Transport ◽  
High Order ◽  
Neutron Transport Equation

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.

The Method of Characteristics for Arbitrary Geometry Based on the Customization of Autocad

2008 ◽  
Author(s):  
Qichang Chen ◽  
Hongchun Wu ◽  
Liangzhi Cao
Keyword(s):  
Boundary Condition ◽  
Transport Equation ◽  
Method Of Characteristics ◽  
Complex Geometry ◽  
Interpolation Method ◽  
Neutron Transport ◽  
Outer Boundary ◽  
Neutron Transport Equation ◽  
The Method Of Characteristics ◽  
Selection Of

The method of characteristics (MOC) solves the neutron transport equation along each characteristics line. It is independent of the geometry shape of boundary and region. So theoretically, this method can be used to solve neutron transport equation in highly complex geometry. However, we should describe the geometry strictly and calculate intersect points of each characteristics line with every boundary and region firstly. In complex geometry, due to the great difficulty of treating of the arbitrary domain, the selection of geometry shape and efficiency of ray tracing are limited. So in most of the existing MOC codes, the type of outer boundary is limited as rectangular, hexagonal, triangular or the combination of them. And in order to treat reflective boundary condition, the selection of the azimuthal angles number is not freewill for different outer boundary shapes. To wipe off these limitations for using MOC in more complex fuel assembly calculation, the more powerful geometry treatment method is needed. The geometry treatment through the customization of AutoCAD, famous computer aided design software, is given in this paper. Thanks to the powerful capability of AutoCAD in graphics, the description of complex geometry becomes quite convenient. Moreover, with the language VBA (Visual Basic for Applications), AutoCAD can be customized to calculate intersect points of each characteristics line with every boundary and region. Thereby, no matter how complex or what kind of the geometry shape is, it can be treated uniformly by this method as long as it can be drawn in the AutoCAD. In addition, a directional interpolation method for the treatment of reflective boundary condition is introduced in this paper, so the number of azimuthal angles can be selected freely.

LTSN solution of the adjoint neutron transport equation with arbitrary source for high order of quadrature in a homogeneous slab

2002 ◽  
Vol 29 (5) ◽  
pp. 561-569 ◽  
Author(s):  
Glenio A. Gonçalves ◽  
Gilberto Orengo ◽  
Marco Tullio M.B. de Vilhena ◽  
Cláudio O. Graça
Keyword(s):  
Transport Equation ◽  
Neutron Transport ◽  
High Order ◽  
Neutron Transport Equation

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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