Recursive solutions for multi-group neutron kinetics diffusion equations in homogeneous three-dimensional rectangular domains with time dependent perturbations
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C. Z. Petersen
, B. E. J. Bodmann , M. T. Vilhena und R. C. Barros
Abstract
In the present work we solve in analytical representation the three dimensional neutron kinetic diffusion problem in rectangular Cartesian geometry for homogeneous and bounded domains for any number of energy groups and precursor concentrations. The solution in analytical representation is constructed using a hierarchical procedure, i. e. the original problem is reduced to a problem previously solved by the authors making use of a combination of the spectral method and a recursive decomposition approach. Time dependent absorption cross sections of the thermal energy group are considered with step, ramp and Chebyshev polynomial variations. For these three cases, we present numerical results and discuss convergence properties and compare our results to those available in the literature.
Kurzfassung
In der vorliegenden Arbeit lösen wir in analytischer Darstellung das dreidimensionale kinetische Neutronendiffusionsproblem in rechtwinkliger kartesischer Geometrie für homogene und begrenzte Gebiete für eine beliebige Anzahl von Energiegruppen und Neutronenvorläuferkonzentrationen. Die Lösung in analytischer Darstellung wird unter Verwendung eines hierarchischen Verfahrens konstruiert, d. h. das ursprüngliche Problem wird zu einem Problem reduziert, welches zuvor von den Autoren unter Verwendung einer Kombination der spektralen Methode und einer rekursiven Zerlegung gelöst wurde. Zeitabhängige Absorptionswirkungsquerschnitte der thermischen Energiegruppe werden mit Sprung-, Rampen-und Tschebyscheff-Polynom Variationen betrachtet. Für diese drei Fälle stellen wir numerische Ergebnisse vor, diskutieren Konvergenzeigenschaften und vergleichen unsere Ergebnisse mit denen in der Literatur.
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Artikel in diesem Heft
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
- Evaluated gas production cross-section data for natural titanium irradiated with protons at energies up to 3 GeV
- Investigation of (n,γ) reaction in hybrid reactor zones
- Burnup analysis of the VVER-1000 reactor using thorium-based fuel
- Equivalent thermal conductivity of the storage basket with spent nuclear fuel of VVER-1000 reactors
- A study on empirical systematic for the (d,n) reaction cross sections at 8.6 MeV
- Recursive solutions for multi-group neutron kinetics diffusion equations in homogeneous three-dimensional rectangular domains with time dependent perturbations
- Thermoluminescent characteristics of nano-structure hydroxyapatite:Dy
- Performance evaluation of anion exchange resins Purolite NRW-5050 and Duolite A-611 by application of radioisotopic techniques
- A binary mixed integer coded genetic algorithm for multi-objective optimization of nuclear research reactor fuel reloading
- Development of an educational nuclear research reactor simulator
- Technical Notes/Technische Mitteilungen
- Obtaining the neutronic and thermal hydraulic parameters of the VVER-1000 Bushehr nuclear reactor core by coupling nuclear codes