We have developed various finite element differencing schemes by applying lumping techniques in neutron streaming and removal terms of the S{sub N} even-parity transport equation in two-dimensional x-y geometry. We have derived an analytical form of the even-parity reflective boundary condition, which along with the vacuum boundary condition can be applied directly to solve second-order even-parity boundary value problems. We have also developed a new simplified even-parity equation that is much more computationally efficient than the even-parity equation. The developed schemes are numerically compared with the conventional first-order diamond-differencing (DD) scheme.
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Los Alamos National Lab., NM (United States)
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New Mexico
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We have developed various finite element differencing schemes by applying lumping techniques in neutron streaming and removal terms of the S{sub N} even-parity transport equation in two-dimensional x-y geometry. We have derived an analytical form of the even-parity reflective boundary condition, which along with the vacuum boundary condition can be applied directly to solve second-order even-parity boundary value problems. We have also developed a new simplified even-parity equation that is much more computationally efficient than the even-parity equation. The developed schemes are numerically compared with the conventional first-order diamond-differencing (DD) scheme.
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Noh, Taewan, Miller, W. F. Jr. & Morel, J. E.Improved approximations applied to the S{sub N} even-parity equation,
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July 1, 1993;
New Mexico.
(https://digital.library.unt.edu/ark:/67531/metadc1341247/:
accessed July 16, 2024),
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