A finite element method for multigroup diffusion-transport problems in two dimensions

Ziver, A.K.; Goddard, A.J.H.

doi:10.1016/0306-4549(81)90136-5

Cited by 13 publications

(1 citation statement)

References 7 publications

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“…(5b) We use the spherical harmonics functions } -1m (JJ) defined by where Ptm(cos 0) are the associated Legendre functions, and {)and ifJ are polar and azimuthal angles of the direction JJ in a polar coordinates. The complex conjugate of Y 1 m(JJ) satisfies the following relation : ( 7) The following orthogonal and recurrence relations hold:…”

Section: (4b)mentioning

confidence: 99%

Solution of Multigroup Transport Equation in X-Y-Z Geometry by the Spherical Harmonics Method Using Finite Fourier Transformation.

Kobayashi

Kikuchi

Tsutsuguchi

1993

J. Nucl. Sci. Technol.

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A neutron multigroup transport equation in x-y-z geometry is solved by the spherical harmonics method using finite Fourier transformation. Using the first term of the Fourier series for the space variables of spherical harmonics moments, three-point finite difference like equations are derived for X-, Y-and z-axis directions, which are more consistent and accurate than those derived using the usual finite difference approximation, and these equations are solved by the iteration method in each axis direction alternatively. A method to find an optimum acceleration factor for this inner iteration is described. It is shown in the numerical examples that the present method gives higher accuracy with less mesh points that the usual finite difference method.

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Section: (4b)mentioning

confidence: 99%