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[en] A special integral equation was derived in previous work using a hybrid diffusion-transport theory method for calculating the flux distribution in slab lattices. In this paper an analytical solution of this equation has been carried out on a finite reactor lattice. The analytical results of disadvantage factors are shown to be accurate in comparison with the numerical results and accurate transport theory calculations. (author)

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[en] A hybrid diffusion-transport theory method for calculating neutron flux distribution in slab lattices is described. A special integral equation is derived which can be solved numerically or analytically. The both methods of solution are shown to give accurate results for disadvantage factors and flux distributions in comparison with accurate transport theory calculations. 8 refs., 4 figs. (author)

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Translated from Atomkernergie Kerntechnik (1985) v. 47(4) p. 222-224.

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Journal Article

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Translation

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Aalam Al-Zarra; CODEN AAALE; (no.8); p. 16-20

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[en] A hybrid diffusion-transport theory method for calculating neutron flux distributions in slab lattices is described. By comparison with accurate transport theory Ssub(N) and collision probability codes it is shown to give accurate results for disadvantage factors and flux distributions for a range of lattices. (orig.)

[de]

Eine hybride Diffusions-Transport-Theorie zur Berechnung der Neutronenflussverteilung in Plattengittern wird beschrieben. Durch Vergleich mit der exakten Ssub(N)-Transporttheorie und Stosswahrscheinlichkeitscodes wird gezeigt, dass die vorgestellte Theorie genaue Erkenntnisse fuer die Nachteilfaktoren und Flussverteilungen einer Reihe von Gittern liefert. (orig.)Primary Subject

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[en] The theory of hybrid principles is presented together with the transformation rule for converting odd-parity approximations into even-parity approximations. This rule leads to a method which provides rigorous upper and lower bounds for the disadvantage factor for a reactor lattice cell. With these bounds very precise benchmarks have been constructed for representative lattices. It is found that a combination of even and odd-parity solutions for the neutron flux is much more efficient than solutions based on either the even-parity or odd-parity. This is the basis of one synthesis scheme. In another synthesis method, a hybrid principle with trial functions for both the even- and odd- parity angular flux is used in conjunction with a classical principle with an odd-parity trial function. The synthesis process is efficient because the largest set of equations to be solved, i.e. the frame work, involves as few as one unknown per node of the finite element mesh. The effectiveness of the synthesis method is demonstrated for a thick shield problem. (author)

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Neutron transport theory

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[en] A family of hybrid variational principles is derived using a generalised least squares method. Neutron conservation is automatically satisfied for the hybrid principles employing two trial functions. No interfaces or reflection conditions need to be imposed on the independent even-parity trial function. For some hybrid principles a single trial function can be employed by relating one parity trial function to the other, using one of the parity transport equation in relaxed form. For other hybrid principles the trial functions can be employed sequentially. Synthesis of transport solutions, starting with the diffusion theory approximation, has been used as a way of reducing the scale of the computation that arises with established finite element methods for neutron transport. (author)

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[en] A lower bound for the disadvantage factor of a lattice cell of arbitrary configuration is obtained using a finite element method which is based on a variational principle for the even-parity angular flux. An upper bound for the disadvantage factor is given by a finite element method using the complementary variational principle for the odd-parity angular flux. These theoretical results are illustrated by calculations for uranium/graphite and uranium/water lattices. As the approximations are refined the fluxes obtained by the first method tend towards the actual flux from below in the moderator, and from above in the fuel. These trends are reversed for the second method. This derivation of benchmarks for disadvantage factors has been undertaken primarily as a test of an important algorithm used by the authors in a method of synthesising transport solutions starting with a diffusion theory approximation. The algorithm is used to convert odd-parity approximations for the angular flux into even-parity approximations and vice versa. (author). 15 refs., 8 tabs., 9 figs

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Translated from Annals of Nuclear Energy (1988) v. 15(5) p. 241-259.

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Journal Article

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Numerical Data; Translation

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Aalam Al-Zarra; CODEN AAALE; (no.14); p. 7-22

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AbstractAbstract

[en] A lower bound for the disadvantage factor of a lattice cell of arbitrary configuration is obtained using a finite element method which is based on a variational principle for the even-parity angular flux. An upper bound for the disadvantage factor is given by a finite element method using the complementary variational principle for the odd-parity angular flux. These theoretical results are illustrated by calculations for urnaium/graphite and uranium/water lattices. As the approximations are refined the fluxes obtained by the first method tend towards the actual flux from below in the moderator, and from above in the fuel. These trends are reversed for the second method. This derivation of benchmarks for disadvantage factors has been undertaken primarily as a test of an important algorithm used by the authors in a method of synthesising transport solutions starting with a diffusion theory approximation. The algorithm is used to convert odd-parity approximations for the angular flux into even-parity approximations and vice versa. (author)

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[en] The solution of problems for large three-dimensional systems by conventional finite element methods is slow, even with the super-computer such as the CRAY. Projection and conservation methods can be used in conjunction to synthesis from a crude approximation a succession of more and more accurate approximations. The conservation method uses an extremum principle with two trial functions; but only one of these, the frame trial function, has to satisfy continuity conditions. When optimised the two trial functions ensure the satisfaction of the neutron conservation condition for each element. Having found a frame trial function the other trial function can be determined element by element. It is then transformed to provide another frame trial function. Extrapolation of these frame functions yields an improved frame trial function to initiate a fresh cycle of approximation. (author). 5 refs., 2 figs., 1 tab

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Translated from 'The mathematics of finite elements and applications VI, Mafelap 1987, edited by J.R. Whiteman, Academic Press Limited, London, 1988.

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Translation

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Aalam Al-Zarra; CODEN AAALE; (no.11); p. 75-77

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