Solution of the neutron diffusion equation at two groups of energy by method of triangular finite elements
Description
The Neutron Diffusion Equation at two groups of energy is solved with the use of the Finite - Element Method with first order triangular elements. The program EFTDN (Triangular Finite Elements on Neutron Diffusion) was developed using the language FORTRAN IV. The discrete formulation of the Diffusion Equation is obtained with the application of the Galerkin's Method. In order to solve the eigenvalue - problem, the Method of the Power is applied and, with the purpose of the convergence of the results, Chebshev's polynomial expressions are applied. On the solution of the systems of equations Gauss' Method is applied, divided in two different parts: triangularization of the matrix of coeficients and retrosubstitution taking in account the sparsity of the system. Several test - problems are solved, among then two P.W.R. type reactors, the ZION-1 with 1300 MWe and the 2D-IAEA - Benchmark. Comparision of results with standard solutions show the validity of application of the EFM and precision of the results. (Author)
Availability note (English)
MF available from INIS under the Report Number.Abstract (Portuguese)
Resolve-se a Equacao de Difusao de Neutrons a dois grupos de energia aplicando-se o Metodo dos Elementos Finitos (MEF), com elementos triangulares de primeira ordem. Para tanto foi desenvolvido o programa EFTDN (Elementos Finitos Triangulares na Difusao de Neutrons) em linguagem FORTRAN IV. A formulacao discreta da Equacao de Difusao e obtida aplicando o metodo de Galerkin. Para resolver o problema de auto-valores e utilizado o metodo da potencia e com a finalidade de acelerar a convergencia dos resultados aplica-se os polinomios de Chebshev. Na solucao dos sistemas de equacoes e aplicado o metodo de Gauss dividido em duas etapas distintas: triangularizacao da matriz dos coeficientes e a retrosubstituicao levando-se em conta a esparsidade do sistema. Alguns problemas teste sao resolvidos, dentre estes dois reatores P.W.R., o ZION-1 de 1300 MWe e o reator 2D-IAEA - Benchmark. Comparando os resultados com as solucoes padroes demonstra-se a validade da aplicacao do MEF e a precisao dos resultados. Discute-se ainda de que forma pode ser melhorado e ampliado este trabalho. (Autor)Files
13703352.pdf
Files
(5.6 MB)
| Name | Size | Download all |
|---|---|---|
|
md5:c84e789d614981b9eb95682825bf93f6
|
5.6 MB | Preview Download |
Additional details
Additional titles
- Original title (Portuguese)
- Solucao da equacao de difusao de neutrons a dois grupos de energia por elementos finitos triangulares
Publishing Information
- Imprint Pagination
- 194 p.
- Report number
- INIS-mf--7385
INIS
- Country of Publication
- Brazil
- Country of Input or Organization
- Brazil
- INIS RN
- 13703352
- Subject category
- S22: GENERAL STUDIES OF NUCLEAR REACTORS;
- Resource subtype / Literary indicator
- Thesis
- Descriptors DEI
- BENCHMARKS; E CODES; FINITE ELEMENT METHOD; GAUSS FUNCTION; MATRIX ELEMENTS; NEUTRON DIFFUSION EQUATION; ZION-1 REACTOR
- Descriptors DEC
- COMPUTER CODES; ENRICHED URANIUM REACTORS; FUNCTIONS; NUMERICAL SOLUTION; POWER REACTORS; PWR TYPE REACTORS; REACTORS; THERMAL REACTORS; WATER COOLED REACTORS; WATER MODERATED REACTORS