The Lattice Boltzmann Methods (LBM) are numerical techniques used to simulate transport phenomena in complex systems. They allow for the modeling of fluid behavior in terms of particles that move on a discrete grid (a "lattice"). Unlike classical methods, which directly solve the differential equations of fluids, LBM simulates the evolution of distribution functions of fluid particles in a discrete space, using propagation and collision rules. The choice of the lattice in LBM is a crucial step, as it directly affects the accuracy, efficiency, and stability of the simulations. The lattice determines how fluid particles interact and move within space, as well as how the discretization of space and time is performed.

LBM methods exhibit natural parallelism properties, as calculations at each grid point are relatively independent. Although classical CFD methods based on the solution of the Navier-Stokes equations can also be parallelized, the nonlinear terms can make parallelism more difficult to manage, especially for models involving turbulent flows or irregular meshes. Therefore, LBM methods allow, at a lower computational cost, to capture complex phenomena. Recent work has shown that it is possible, with LBM, to reproduce the Nukiyama cooling curve (boiling in a vessel) and thus accurately calculate the critical heat flux. This flux corresponds to a mass boiling, known as the boiling crisis, which results in a sudden degradation of heat transfer.

The critical heat flux is a crucial issue for the Jules Horowitz Reactor, as experimental devices (DEX) are cooled by water in either natural or forced convection. Therefore, to ensure proper cooling of the DEX and the safety of the reactor, it is essential to ensure that, within the studied parameter range, the critical heat flux is not reached. It must therefore be determined with precision.

In the first part of the study, the student will define a lattice to apply LBM methods on an RJH device in natural convection. The student will then consolidate the results by comparing them with available data. Finally, exploratory calculations in forced convection (from laminar to turbulent flow) will be conducted.