A comparative study on classical polynomial approximations to the transport equation in spherical media albedo problems
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A. Yılmazer
Abstract
The ultraspherical polynomial approximation which unifies all classical polynomial sequences in a unique form is used to calculate the albedo for isotropic scattering in a homogeneous spherical medium. This is the most general polynomial approach in the sense that it includes all classical polynomial methods to solve the transport equation such as and methods. For the first time an antisymmetric polynomial (ultraspherical polynomial) solution to the corresponding pseudo-slab problem is proposed. Very accurate and consistent albedo values are obtained for a variety of methods when compared to the literature. It is also shown that various approximations differ only in convergency characteristics; some converge monotonically, some in the mean.
Kurzfassung
Die ultrasphärische Polynom Approximation, die alle klassischen polynomiellen Folgen vereinheitlicht, wird zur Berechnung der Albedo für isotrope Streuung in einem homogenen kugelförmigen Medium verwendet. Dies ist der allgemeinste Polynomansatz, der alle klassichen polynomiellen Methoden zur Lösung der Transportgleichung, wie zum Beispiel und Methoden umfasst. Zum ersten Mal wird eine antisymmetrische polynomielle Lösung (ultrasphärische Polynome) für das Pseudo-Platten Problem vorgeschlagen. Man erhält sehr genaue und konsistente Albedo-Werte für verschiedene Methoden verglichen mit Werten aus der Literatur. Es wird außerdem gezeigt, dass sich verschiedene Approximationen nur in ihren Konvergenzeigenschaften unterscheiden; einige konvergieren monoton, andere im Mittel.
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© 2008, Carl Hanser Verlag, München
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- Re-evaluation of the criticality experiments of the “Otto Hahn Nuclear Ship” reactor
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- Unified treatment of the P(λ)n approximation to solve the reflected slab criticality problem with strong anisotropy
- A comparative study on classical polynomial approximations to the transport equation in spherical media albedo problems
- Solution of half space and slab albedo problems for linearly anisotropic scattering with the modified FN method
- Study of the effect of anisotropic scattering on the critical slab problem in neutron transport theory using Chebyshev polynomials
Articles in the same Issue
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
- Development and validation of the pressure surge computer code DYVRO mod. 3
- Simulation model of a nuclear power plant turbine
- Study on the thermal-hydraulics characteristics of a boiling two-phase natural circulation loop with nanofluids
- The effect of combination of different materials on neutron absorption in a nuclear research reactor spent fuel pool
- Re-evaluation of the criticality experiments of the “Otto Hahn Nuclear Ship” reactor
- Potential advantages and disadvantages of sequentially building small nuclear units instead of a large nuclear plant
- Radiological consequences of potential sabotage attack to storage casks on the ISFSI site
- Unified treatment of the P(λ)n approximation to solve the reflected slab criticality problem with strong anisotropy
- A comparative study on classical polynomial approximations to the transport equation in spherical media albedo problems
- Solution of half space and slab albedo problems for linearly anisotropic scattering with the modified FN method
- Study of the effect of anisotropic scattering on the critical slab problem in neutron transport theory using Chebyshev polynomials
