An analytic solution method for discrete ordinates transport equations in slab geometry with no spatial truncation error
Recently, some authors have devised exact methods with no spatial truncation error for solving the slab geometry discrete ordinates problems. First, Barros and Larsen developed the spectral Green's function (SGF) method where an exact relation between cell-edge and cell-average angular fluxes is derived by using a spectral analysis (i.e., obtaining eigenfunctions). Second, a direct method was developed by using the Laplace transform. More generally in continuous angle, the Fourier transform and inversion were used to provide analytical benchmark solutions. While motivated by Ref. 1, the authors present a new method that gives exact solutions (with no spatial truncation error) of the one-group discrete ordinates transport equations in slab geometry. The method is based on the infinite medium Green's function (IMGF) and Placzek's lemma. The IMGF is derived analytically by spectral analysis. The method yields concise equations resulting in an economical algorithm. The method does not require a set of intermediary parameters that are used in the SGF method and should be solved numerically from a system of linear equations. The unknowns are cell-edge angular fluxes in the present method, whereas in the SGF method there are two types of unknowns: cell-edge and cell-average angular fluxes. In addition, the present method easily allows the source to be distributed arbitrarily in space. Once the final equation for cell-edge angular fluxes is solved, the analytic solution is easily represented in terms of the cell-edge angular fluxes. The numerical results show that the method gives exact solutions of the discrete ordinates equations, independent of mesh size.
- Research Organization:
- Korea Advanced Inst. of Science and Technology, Seoul (KR)
- OSTI ID:
- 20005772
- Journal Information:
- Transactions of the American Nuclear Society, Vol. 81; Conference: American Nuclear Society 1999 Winter Meeting, Long Beach, CA (US), 11/14/1999--11/18/1999; Other Information: PBD: 1999; ISSN 0003-018X
- Country of Publication:
- United States
- Language:
- English
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