Solution of the Multigroup-Diffusion equation by the response matrix method
Description
A preliminary analysis of the response matrix method is made, considering its application to the solution of the multigroup diffusion equations. The one-dimensional formulation is presented and used to test some flux expansions, seeking the application of the method to the two-dimensional problem. This formulation also solves the equations that arise from the integro-differential synthesis algorithm. The slow convergence of the power method, used to solve the eigenvalue problem, and its acceleration by means of the Chebyshev polynomial method, are also studied. An algorithm for the estimation of the dominance ratio is presented, based on the residues of two successive iteration vectors. This ratio, which is not known a priori, is fundamental for the efficiency of the method. Some numerical problems are solved, testing the 1D formulation of the response matrix method, its application to the synthesis algorithm and also, at the same time, the algorithm to accelerate the source problem. (Author)
Availability note (English)
MF available from INIS under the Report Number.Abstract (Portuguese)
Uma analise preliminar do metodo de matrizes resposta e feita, com relacao a sua aplicacao na solucao das equacoes multigrupo-difusao. A formulacao a uma dimensao e apresentada e utilizada para testar alguns tipos de expansoes para o fluxo, com vistas a solucao do problema a duas dimensoes por este metodo. Esta formulacao resolve ainda, as equacoes que surgem do algoritmo da sintese integro-diferencial. A convergencia lenta do metodo da potencia, utilizado na solucao do problema de autovalor, e sua aceleracao atraves do metodo dos polinomios de Chebyshev, tambem sao estudadas. Um algoritmo para a estimativa da razao de dominancia e apresentado, baseando-se no residuo dos vetores de duas iteracoes sucessivas. Esta razao, que nao e conhecida a priori, e fundamental para a eficiencia do metodo. Alguns problemas foram resolvidos numericamente de modo a testar a formulacao 1D do metodo de matrizes resposta, sua aplicacao a sintese e, ao mesmo tempo, o algoritmo para a aceleracao do problema de fonte. (Autor)Files
14724849.pdf
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Additional details
Additional titles
- Original title (Portuguese)
- Solucao das equacoes Multigrupo-Difusao pelo metodo de matrizes resposta
Publishing Information
- Imprint Pagination
- 88 p.
- Report number
- INIS-mf--7723
INIS
- Country of Publication
- Brazil
- Country of Input or Organization
- Brazil
- INIS RN
- 14724849
- Subject category
- S22: GENERAL STUDIES OF NUCLEAR REACTORS;
- Resource subtype / Literary indicator
- Thesis
- Descriptors DEI
- MULTIGROUP THEORY; NEUTRON TRANSPORT THEORY; NUMERICAL SOLUTION; ONE-DIMENSIONAL CALCULATIONS
- Descriptors DEC
- TRANSPORT THEORY