A Semi-Analytical Solution to Milne Problem in the Case of Multiple Synthetic Scattering

Haggag, M. H.; Machali, H. M.

doi:10.9790/4861-06631116

Cited by 2 publications

(2 citation statements)

References 16 publications

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“…The scattering Kernel, introduced by İnönü [13], is a combination of forward, backward, and isotropic scattering. It was used to solve radiative transfer problems in one region in many papers [14][15][16]. Haggag and Machali [16]; solved the Milne problem in the case of multiple synthetic scattering.…”

Section: Introductionmentioning

confidence: 99%

“…It was used to solve radiative transfer problems in one region in many papers [14][15][16]. Haggag and Machali [16]; solved the Milne problem in the case of multiple synthetic scattering. Ersoy et al [17] used the facil (FN) method to solve the neutron transport equation for the Milne problem with a linear combination of the forward, backward, and isotropic scattering kernel (FBIS kernel).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Study of Forward and Backward Scattering in Two-Region Milne Problem for Non-Absorbing Medium Using a Synthetic Kernel

Garbiea¹,

El-Depsy

Selim

et al. 2023

Preprint

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In this work, the effect of an extremely anisotropic scattering function on the two-region Milne problem is studied. This scattering function divides the neutrons resulting from the collisions into three parts; part (í µí±) which moves backward, part (m) which moves forward, and part (n) which emerge isotropically from the collisions, where í µí±+m+n=1. The integral version of the transport equation is solved using trial functions based on Case’s eigenmodes and exponential integral function. Hence, the solution to the Milne problem is formulated in terms of characteristic quantities such as the extrapolation length and the fractional scalar flux discontinuity. Numerical results for the analytically evaluated quantities are presented. Some of our numerical results are compared with the available published results.

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