Investigation of efficient and reliable numerical algorithms for coupled reactor calculations X-TREAM project: Task 1b Survey of the state-of-the-art numerical techniques for solving coupled non-linear multi-physics equations

Nowadays, the precise modeling of a nuclear reactor core is a challenge. This task involves several aspects, from the computational power needed to perform simulations, to the physics and analysis of the outcome. The need to better understand the physical phenomena is critical in order to quantify and qualify nuclear safety parameters. Currently, substantial research has been done in order to optimize the prediction capabilities of coupled codes. The need to better understand the multi-physics coupling between the neutronics and the thermal-hydraulics is required. In this report, state-of-the art of current methods and numerical techniques used in coupled codes are highlighted. A better understanding of the numerical schemes will allows selecting an appropriate algorithm to be implemented in POLCA-T. POLCA-T is the coupled code developed by Westinghouse that currently uses an explicit approach to couple the neutronics (POLCA7) and thermal-hydraulics (RIGEL). The final objective is to implement the concept of the Jacobian-free Newton-Krylov method, which will be used for solving the nonlinear equations which rise from the coupled solution.