The Optimal Theta of Optimally Diffusive Coarse Mesh Finite Difference Method to Accelerate DGFEM Based SN

Abstract

Abstract Optimally diffusive coarse mesh finite difference (odCMFD) method is a recently developed acceleration method for neutron transport equation. Compared with the traditional CMFD, it adds an optimal theta on the diffusion coefficient. This new acceleration method achieves a higher convergence rate than the traditional CMFD and promises the convergence even in large optical thickness region. However, the optimal theta of odCMFD is determined by the Fourier analysis results of the 1D traditional SN. When applying the odCMFD to accelerate DGFEM based SN, this optimal theta is not always suitable. Therefore, it is necessary to find a new optimal theta for this new scheme. In this paper, a Fourier analysis of DGFEM based SN using odCMFD acceleration for k-eigenvalue neutron transport problem is conducted. Fourier analysis results show that when the number of inner iterations is higher than 10, the increment of the inner iterations has little impact on the spectral radius. Meanwhile, the order of the DGFEM based SN and the order of SN quadrature set have little impact on the spectral radius. The scattering ratio has great impact on the spectral radius, the decrement of scattering ratio increases the spectral radius. Set the number of inner iterations as 10, for different scattering ratio, an optimal theta of odCMFD and a polynomial fitting curve are obtained by Fourier analysis. Finally, numerical estimations of spectral radius are obtained by real 1D DGFEM based SN calculation with odCMFD acceleration. The experiment values fit well with the Fourier analysis theoretical results.