Theoretical Convergence Study of lpCMFD for Fixed Source Neutron Transport Problems in 2D Cartesian Geometry

2019 ◽  
Author(s):  
Y. Chan ◽  
S. Xiao
Keyword(s):  
Neutron Transport ◽  
Source Neutron ◽  
Cartesian Geometry ◽  
Convergence Study ◽  
Transport Problems

scholarly journals Formulação nodal aplicada à problemas de transporte bidimensional em geometria cartesiana

2015 ◽  
Vol 11 (8) ◽  
Author(s):  
Carlos Eduardo Souza Ferreira ◽  
Leonardo Ramos Emmendorfer ◽  
João Francisco Prolo Filho
Keyword(s):  
Neutron Transport ◽  
Computational Cost ◽  
Coupled System ◽  
Two Dimensional ◽  
Discrete Ordinate ◽  
One Dimensional ◽  
Scalar Fluxes ◽  
Cartesian Geometry ◽  
Transport Problems ◽  
Low Computational Cost

<div><p class="SPabstract">Neste trabalho, uma formulação nodal é proposta para o tratamento de uma classe de problemas de transporte de nêutrons, em geometria cartesiana bidimensional. Através do processo de integração, equações unidimensionais são obtidas, reescrevendo o modelo em termos de quantidades médias. A resolução das equações integradas é feita através de uma versão do método de Ordenadas Discretas Analítico (ADO), onde também são obtidas soluções explicitas, analíticas em termos das variáveis espaciais, através de um código de fácil implementação. Pode-se destacar também como vantagens desta formulação a versatilidade na escolha da quadratura e o baixo custo computacional, uma vez que esquemas iterativos não são necessários tampouco a subdivisão do domínio em células. Para lidar como os termos do contorno que surgem no processo, propõe-se aqui uma representação por constantes, de forma que as equações nas variáveis x e y são tratadas através de um sistema acoplado. Resultados obtidos por esta formulação são apresentados, bem como alguns perfis de fluxos escalares. </p></div><p><strong>Nodal formulation applied to two-dimensional transport problems in Cartesian geometry.</strong></p><p> In this paper, a nodal formulation is proposed for the treatment of a class of neutron transport problems in two-dimensional Cartesian geometry. By the integration process, one-dimensional equations are obtained, rewriting the model in terms of average quantities. The resolution of the integrated equations is made using a version of the Analytical Discrete Ordinate method (ADO), where also be obtained explicit solutions, analytical in terms of spatial variables, through an easy implementation code. It can also highlight as advantages of this formulation the versatility of the quadrature choice and the low computational cost, since iterative schemes are not needed either subdividing the domain in cells. To deal with the contour terms that arise in the process, is proposed here a representation by constants, so that the equations in the variables x and y are treated through a coupled system. Results obtained by this formulation are presented, as well as some profiles of scalar fluxes. </p>

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

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

Behavior of a Sequence of Geometric Transformations for a Truncated Ellipsoid Geometry in Transport Theory

2009 ◽  
Author(s):  
Rube´n Panta Pazos
Keyword(s):  
Boundary Conditions ◽  
Symmetry Axis ◽  
Transport Theory ◽  
Neutron Transport ◽  
Complex Function ◽  
Computational Techniques ◽  
Neutron Transport Equation ◽  
Geometric Transformations ◽  
The Right ◽  
Transport Problems

The neutron transport equation has been studied from different approaches, in order to solve different situations. The number of methods and computational techniques has increased recently. In this work we present the behavior of a sequence of geometric transformations evolving different transport problems in order to obtain solve a transport problem in a truncated ellipsoid geometry and subject to known boundary conditions. This scheme was depicted in 8, but now is solved for the different steps. First, it is considered a rectangle domain that consists of three regions, source, void and shield regions 5. Horseshoe domain: for that it is used the complex function: f:D→C,definedasf(z)=12ez+1ezwhereD=z∈C−0.5≤Re(z)≤0.5,−12π≤Im(z)≤12π(0.1) The geometry obtained is such that the source is at the focus of an ellipse, and the target coincides with the other focus. The boundary conditions are reflective in the left boundary and vacuum in the right boundary. Indeed, if the eccentricity is a number between 0,95 and 0,99, the distance between the source and the target ranges from 20 to 100 length units. The rotation around the symmetry axis of the horseshoe domain generates a truncated ellipsoid, such that a focus coincides with the source. In this work it is analyzed the flux in each step, giving numerical results obtained in a computer algebraic system. Applications: in nuclear medicine and others.

A POD reduced-order model for resolving the neutron transport problems of nuclear reactor

2020 ◽  
Vol 149 ◽  
pp. 107799
Author(s):  
Yue Sun ◽  
Junhe Yang ◽  
Yahui Wang ◽  
Zhuo Li ◽  
Yu Ma
Keyword(s):  
Nuclear Reactor ◽  
Neutron Transport ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Transport Problems
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