Convergence rate of interface flux iteration for one-dimensional simplified S{sub N} method
Recently, we presented a method called the simplified S{sub N} method for the (numerical) solution of one-group plane geometry S{sub N} problems with an arbitrary anisotropic scattering order of L (L {le} N - 1). The simplified S{sub N} SS{sub N} method, completely free from all spatial truncation errors, is based on the expansion of the angular flux in spherical harmonic (P{sub N - 1}) solutions. The analytic expression for the angular flux for each discrete ordinates direction depends on the exponential functions, arbitrary constants, and the interior source. The outgoing angular fluxes in each spatial cell for each discrete ordinates direction are defined in terms of Green`s function, the incoming angular fluxes from all directions, and the interior source. The only unknowns in the method are the outgoing angular fluxes that do not depend on the scattering source. The outgoing (interface) angular fluxes are computed using an iterative scheme called the interface flux iteration (IFI). Our earlier experimental experience indicates that the convergence rate of the SS{sub N} method with the IFI (SS{sub N} + IFI) for coarse meshes is much faster than that of the conventional S{sub N} (CS{sub N}) method with source iteration (SI). However, as the mesh size goes to zero, the convergence rate of the SS{sub N} + IFI is about the same as that of the CS{sub N} method with SI CS{sub N} + SI. In this study, we perform a Fourier analysis to theoretically predict the convergencc rate of the SS{sub N} + IF1 scheme and compare it with the experimental results.
- OSTI ID:
- 89139
- Report Number(s):
- CONF-941102-; ISSN 0003-018X; TRN: 95:004215-0212
- Journal Information:
- Transactions of the American Nuclear Society, Vol. 71; Conference: Winter meeting of the American Nuclear Society (ANS), Washington, DC (United States), 13-18 Nov 1994; Other Information: PBD: 1994
- Country of Publication:
- United States
- Language:
- English
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