Angular Adaptive Algorithm Based On Discontinuous Finite Element Quadrature Sets On Icosahedron

High-precision shielding calculation is a significant design basis for the shielding design of nuclear devices.The discrete ordinates method(SN)is currently the most widely used deterministic shielding calculation method at home and abroad.SN method employs discrete quadrature sets to approximate the neutron flux.However,traditional quadrature sets have insufficient local integration capability,and it is not adaptable to the shielding problems with strong angular flux anisotropy,resulting in larger angular discretization errors which seriously affect the accuracy and reliability of deterministic methods.Based on the idea of discontinuous finite element,this paper has developed a new discontinuous finite element discrete quadrature set based on regular icosahedron,expanding the local integration capability of traditional quadrature sets.The angular adaptive method have combined with the new quadrature sets to better adapt to duct shielding problems,which can effectively balance the calculation efficiency and accuracy.This quadrature sets generate discrete directions by inscribing icosahedron onto the spherical surface,and integral basis functions in the corresponding discrete regions are used as weight coefficients.The quadrature sets optimization techniques are used to ensure that the weights are strictly non-negative.The angular adaptive algorithm is based on the posterior discrete error estimation,and uses the spherical harmonics method interpolation and the current numerical solution to calculate the error distribution as the basis for the adaptive judgment to achieve local refinement in the one-twentieth angle area.The discontinuous finite element quadrature sets based on icosahedron have advantages such as large number of discrete directions,strictly non-negative weights,local refined easily,and high integration accuracy in the local angle region.The numerical results show that this quadrature sets can accurately integrate the corresponding and below orders of the spherical harmonic function in the one-twentieth sphere,and have fourth-order convergence.When the number of discrete directions are the same or similiar,the numerical accuracy of the discontinuous finite element quadrature sets based on the icosahedron is higher than that of the traditional quadrature sets.For different shielding models.the angular adaptive method can generate a reasonable and efficient angular discrete distribution,control the discrete error,and further improve the calculation efficiency.The calculation time of the angular adaptive method in Kobayashi benchmark problem 2 is only 1/8 of the uniform quadrature sets.In the experimental duct problem of Technical University of Budapest research reactor,the relative error between the calculated value and the experimental value is within 12%,the neutron energy spectrum agrees well with the experimental value,and the neutron flux distribution is reasonable throughout the model.The research in this paper expands the local integration capability of traditional quadrature sets,and it is helpful to solve the problem of excessive angular discretization error in the duct shielding problems,which has certain engineering application prospects.