A two-dimensional finite element shielding calculation code with mass-matrix lumping technique and unstructured meshes

Abstract

BackgroundThe high-fidelity neutron transport calculation requires refined geometric modeling whilst the unstructured meshes have strong adaptability to copy with the changes bring by complex geometry structure, and overcome the deficiencies of structured meshes in modeling capability.PurposeThis study aims to develop and validate a two-dimensional shielding calculation code ThorSNIPE which can be used to improve the modeling ability for analysis complex problems.MethodsFirst of all, problem solving model was established with discrete ordinates method and finite element method on the basis of the first order Boltzmann transport equation. The computational performance of continuous finite element method and discontinuous finite element method were compared and analyzed. Mass-matrix lumping technique was further applied to improve the reliability of solving model. Then, a two-dimensional discrete ordinate-finite element shielding calculation program ThorSNIPE was developed on the basis of above model. Finally, the code was validated by BWR cell critical benchmark, Argonne-5-A1 fixed source benchmark and Dog leg duct benchmark.Results & ConclusionsThe numerical results show that calculation value provided by ThorSNIPE is in good agreement with reference value, indicating that ThorSNIPE is suitable for complex shielding calculation, and Mass-matrix lumping technique can effectively suppress the non-physical spatial oscillations without reducing the calculation accuracy.

Keywords

• shielding calculation
• discrete ordinates method
• finite element method
• unstructured meshes
• mass-matrix lumping technique