In this study, we developed a neutron diffusion equation solver based on the finite element method for CAPP code. Three types of triangular finite elements and five types of rectangular depending on the order of the shape functions were implemented for 2-D application. Ten types of triangular prismatic finite elements and seventeen types of rectangular prismatic finite elements were also implemented for 3-D application. Two types of polynomial mapping from the master finite element to a real finite element were adopted for flexibility in dealing with complex geometry. They are linear mapping and iso-parametric mapping. In linear mapping, only the vertex nodes are used as the mapping points. In iso-parametric mapping, all the nodal points in the finite element are used as the mapping points, which enables the real finite elements to have curved surfaces. For the treatment of spatial dependency of cross-sections in the finite elements, three types of polynomial expansion of the cross-sections in the finite elements were implemented. They are constant, linear, and iso-parametric cross-section expansions. The power method with the Wielandt acceleration technique was adopted as the outer iteration algorithm. The BiCGSTAB algorithm with the ILU (Incomplete LU) decomposition preconditioner was used as the linear equation solver in the inner iteration. The neutron diffusion equation solver developed in this study was verified against two well known benchmark problems, IAEA PWR benchmark problem and OECD/NEA PBMR400 benchmark problem. Results of numerical tests showed that the solution converged to the reference solution as the finite elements are refined and as the order of the finite elements increases. Numerical tests also showed that the higher order finite element method is much efficient than lower order finite element method or finite difference method.
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Fourth International Topical Meeting on High Temperature Reactor Technology
September 28–October 1, 2008
Washington, DC, USA
Conference Sponsors:
- ASME
ISBN:
978-0-7918-4854-8
PROCEEDINGS PAPER
Development of the CAPP Code Based on the Finite Element Method for the Analysis of VHTR Cores
Hyun Chul Lee,
Hyun Chul Lee
Korea Atomic Energy Research Institute, Daejeon, South Korea
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Chang Keun Jo,
Chang Keun Jo
Korea Atomic Energy Research Institute, Daejeon, South Korea
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Jae Man Noh
Jae Man Noh
Korea Atomic Energy Research Institute, Daejeon, South Korea
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Hyun Chul Lee
Korea Atomic Energy Research Institute, Daejeon, South Korea
Chang Keun Jo
Korea Atomic Energy Research Institute, Daejeon, South Korea
Jae Man Noh
Korea Atomic Energy Research Institute, Daejeon, South Korea
Paper No:
HTR2008-58169, pp. 531-538; 8 pages
Published Online:
July 1, 2009
Citation
Lee, HC, Jo, CK, & Noh, JM. "Development of the CAPP Code Based on the Finite Element Method for the Analysis of VHTR Cores." Proceedings of the Fourth International Topical Meeting on High Temperature Reactor Technology. Fourth International Topical Meeting on High Temperature Reactor Technology, Volume 1. Washington, DC, USA. September 28–October 1, 2008. pp. 531-538. ASME. https://doi.org/10.1115/HTR2008-58169
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