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Application of the hierarchical domain decomposition boundary element method to the simplified P$$_{3}$$ equation

階層領域分割型境界要素法のSP$$_{3}$$方程式への適用

千葉 豪

Chiba, Go

中性子拡散方程式の解法として開発された階層領域分割型境界要素法(HDD-BEM)を簡易P$$_{3}$$方程式(SP$$_{3}$$方程式)に適用した。SP$$_{3}$$方程式に対するHDD-BEMの解法を論文中に示した。HDD-BEMに基づく計算プログラムABEMIEを開発し、その妥当性を確認するため二次元一群非等方散乱のベンチマーク問題を解いた。ベンチマーク計算の結果、実効増倍率及び中性子束分布について、本手法が有限要素法に基づく既存の計算プログラムによる参照解とよく一致することを示した。これにより、HDD-BEMがSP$$_{N}$$方程式の有効な解法となりえることを示した。

In the present paper, the hierarchical domain decomposition boundary element method (HDD-BEM), which has been developed to solve the diffusion equation, is applied to the simplified P$$_{3}$$ (SP$$_{3}$$) equation. The solution methodology of the HDD-BEM for the SP$$_{3}$$ equation is provided in the present paper. A computer program ABEMIE based on the HDD-BEM is developed, and a two-dimensional one-group anisotropic scattering benchmark problem is solved with it to verify the present HDD-BEM for the SP$$_{3}$$ equation. Through numerical benchmarking, it is shown that the present method results in good agreement with the solution obtained by using the existing SP$$_{N}$$ solver based on the finite element method for both eigenvalue and neutron flux distribution. This benchmark result suggests that the HDD-BEM can be an efficient solver for the SP$$_{N}$$ equation.

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