Stability and Performance of the X-CMFD Method for Multiphysics Reactor Calculations

This paper presents an innovative approach to efficiently perform deterministic direct whole-core transport calculations with multiphysics feedback for steady-state problems. Traditionally, Picard iteration combined with coarse mesh finite difference (CMFD) acceleration has been used, but it can suffer from instability and inefficiency in certain scenarios. In this work, we introduce the X-CMFD method, supported by Fourier analysis, to enhance the stability of the multiphysics iteration scheme. A new and efficient variation of the X-CMFD method for practical simulations is also present. Additionally, we explore the theoretical convergence rates of nonlinear fully coupled diffusion acceleration (NFCDA), a class of diffusion acceleration methods that formalizes similar ideas of previous research. NFCDA uses a low-order diffusion problem that is fully coupled with equivalent nonlinear multiphysics feedback to accelerate the high-order transport problem with feedback. The theoretical analysis shows that NFCDA offers similar convergence rates to nonlinear diffusion acceleration (NDA) in problems without feedback. This provides theoretical support for numerical experiments conducted by other researchers. X-CMFD, which is a discretized form of NFCDA, leverages typical coarse mesh concepts and operators from CMFD while applying feedback to cross sections in the low-order diffusion problem at each power iteration of the low-order problem. To reduce computational costs, we optimize the implementation of X-CMFD in MPACT by introducing an equivalent low-order approximation to the cross-section updates in the nonlinear low-order problem. Numerical results from pressurized water reactor problems demonstrate that X-CMFD, along with its practical implementation, outperforms current relaxed Picard iteration methods in terms of robustness and efficiency, irrespective of the presence of multiphysics feedback.