A semi-analytic multigroup nodal method

Kim, Yeong-Il; Kim, Young‐Jin; Kim, Sang-Ji; Kim, Taek-Kyum

doi:10.1016/s0306-4549(98)00088-7

“…In order to take this advantage and the generic advantage of SANM, the source expansion form of SANM is employed in this work. Like in Kim's work, 5) a quartic expansion of the source is to be used in order to avoid the error associated with a low-order source expansion. However, the source expansion coefficients will be determined differently such that the third and fourth moments of the fluxes can be used to enhance the accuracy of the approximation.…”

Section: Introductionmentioning

confidence: 99%

Two-Level Coarse Mesh Finite Difference Formulation with Multigroup Source Expansion Nodal Kernels

Yoon¹,

Joo²

2008

J. Nucl. Sci. Technol.

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As an effort to establish a fast, yet accurate multigroup nodal solution method that is crucial in repeated static and transient calculations for advanced reactors, the source expansion form of the semi-analytic nodal method (SANM) is introduced within the framework of the coarse mesh finite difference (CMFD) formulation. The source expansion is to expand the analytic form of the source appearing in the groupwise neutron diffusion equation with a set of orthogonal polynomials in order to obtain a group decoupled analytic solution. Both one-and two-node formulations are examined to determine the best nodal kernel. For the acceleration, a two-level CMFD scheme is established employing a multigroup and two-group CMFD. In addition, an alternative two-node direct SANM formulation with a quartic polynomial is examined to assess the direct vs. iterative resolution of the group coupling. The performance of the CMFD formulation with three different multigroup SANM nodal kernels is examined for a wide variety of multigroup benchmark problems including several MOX-loaded LWR cores and large FBR cores. It is demonstrated that superior accuracy is achievable with all the SANM kernels while the iterative two-node SANM kernel outperforms the others in the multigroup calculations employing more than two groups, and the two-level CMFD formulation is quite efficient in the acceleration of the outer iteration.

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“…2) This method was later applied to a spatial kinetics code, NLSANMT, by Liao and Xie. 4) There was a variant of SANM called SANEM (semi-analytic nodal expansion method) developed by Kim et al 5) Kim used a quartic polynomial representation of the source so that the groupwise flux solution consists of a 4th-order polynomial particular solution and sinh and cosh homogeneous solutions. In order to determine the source expansion coefficients, Kim used exactly the same method as the one used in the NEM formulation, which uses a node average value, two surface values, and two weighted residual conditions.…”

Section: Introductionmentioning

confidence: 99%

Two-Level Coarse Mesh Finite Difference Formulation with Multigroup Source Expansion Nodal Kernels

Yoon

¹

,

Joo

²

2008

Journal of Nuclear Science and Technology

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As an effort to establish a fast, yet accurate multigroup nodal solution method that is crucial in repeated static and transient calculations for advanced reactors, the source expansion form of the semi-analytic nodal method (SANM) is introduced within the framework of the coarse mesh finite difference (CMFD) formulation. The source expansion is to expand the analytic form of the source appearing in the groupwise neutron diffusion equation with a set of orthogonal polynomials in order to obtain a group decoupled analytic solution. Both one-and two-node formulations are examined to determine the best nodal kernel. For the acceleration, a two-level CMFD scheme is established employing a multigroup and two-group CMFD. In addition, an alternative two-node direct SANM formulation with a quartic polynomial is examined to assess the direct vs. iterative resolution of the group coupling. The performance of the CMFD formulation with three different multigroup SANM nodal kernels is examined for a wide variety of multigroup benchmark problems including several MOX-loaded LWR cores and large FBR cores. It is demonstrated that superior accuracy is achievable with all the SANM kernels while the iterative two-node SANM kernel outperforms the others in the multigroup calculations employing more than two groups, and the two-level CMFD formulation is quite efficient in the acceleration of the outer iteration.

show abstract