Stability analysis of the CMFD scheme with linear prolongation

Highlights: • Thorough Fourier analysis on lpCMFD. • An unconditionally stable variant of lpCMFD. • Comprehensive comparison with CMFD methods. - Abstract: The stability analysis was performed on a new CMFD method (lpCMFD) for both k-eigenvalue problem (EVP) and transient fixed source problem (TFSP), and an unconditionally stable variant of lpCMFD method was presented in this paper. The lpCMFD is a new CMFD method which updates the fine cell scalar flux via linear prolongation of local and neighboring coarse mesh fluxes. The stability analysis was performed on the $S_N$-lpCMFD scheme using the Fourier analysis approach. The theoretical results agree well with numerical results. The lpCMFD presented here is shown to be more stable than the conventional CMFD (fpCMFD) method where flat prolongation is used. The unconditionally stable variant of lpCMFD is developed based on the fine cell optical thickness threshold and the insights provided by the optimal diffusive CMFD (odCMFD). The new method is referred to as stabilized CMFD with linear prolongation (SlpCMFD) and is shown to converge faster than all mainstream CMFD methods.