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Investigating a Matrix-free, Newton-based, Neutronic-Monte Carlo/Thermal-Hydraulic Coupling Scheme

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In the field of nuclear reactor analysis, multiphysics calculations that account for the bonded nature of the neutronic and thermal-hydraulic phenomena are of major importance for both reactor safety and design. So far in the context of Monte-Carlo neutronic analysis, the Gauss-Seidel iterative scheme, in a version for individual single-physics solvers, is mainly used for coupling with thermal-hydraulics. This work investigates the possibility of replacing the previous scheme with an approximate Newton algorithm. The proposed method, called Approximate Block Newton, is actually a version of the Jacobian-free Newton Krylov method suitably modified for coupling mono-disciplinary solvers. Within this Newton scheme the linearised system is solved with a Krylov solver in order to avoid the need for creation of the Jacobian matrix. Main motivation for this approach is the interest for an algorithm that could maintain the distinct treatment of the involved fields within a tight coupling context. This work performs preliminary analysis in order to investigate the behaviour of the proposed method in reactor analysis. More specifically, OpenMC, a Monte-Carlo neutronic code and COBRA-EN, a thermal hydraulic code for sub-channel and core analysis, are merged in a coupling scheme using the Approximate Block Newton method with the aim to examine the performance and the accuracy of this coupling scheme and compare with those of the traditional sequential iterative scheme.
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... As the convergence of an algorithm is always an important issue, an improvement of the convergence behaviour by adopting a new numerical technique (Approximate Block Newton method) and developing an innovative neutronic-MC/T-H coupling scheme, was attempted. It was found that the proposed coupling methodology outperforms the traditional sequential one as shown in [40]. The improvement seems to be more significant in the BWR cases, however further investigation especially in larger scale problems is needed in order to exploit in more detail the features, the advantages and disadvantages of this innovative coupling scheme. ...
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