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Reactor design requires safety studies to ensure that the reactors will behave appropriately under incidental or accidental situations. Safety studies often involve multiphysics simulations where several branches of reactor physics are necessary to model a given phenomenon. In those situations, it has been observed that the neutron transport part is still a bottleneck in terms of computational times, with more than 80% of the total time. In the case of hexagonal lattice reactors, transport solvers usually invert the discretised Boltzmann equation by discretising the regular hexagon into lozenges or triangles. In this work, we seek to reduce the computational burden of the neutron transport solver by designing a numerical spatial discretisation scheme that would be more appropriate for honeycomb meshes. In our past research efforts, we have set up interesting discretisation schemes in the finite element setting in 2D, and we wish to extend them to 3D geometries that are prisms with a hexagonal base. In 3D, a rigorous method was derived to shrink the tensor product between 2D and 1D bases to minimum terms. We have applied these functions successfully on a reactor benchmark—Takeda Model 4—to compare and contrast the numerical results in a physical setting. [ABSTRACT FROM AUTHOR]

Presently, APOLLO3® /MINARET solves the transport equation using the multigroup Sn method with discontinuous finite elements on triangular meshes with Lagrange polynomial bases. The goal of this work is to solve the spatial problem on hexagonal geometries in the context of honeycomb lattice reactors, without further refining the computational mesh. The idea here is to construct high-order basis functions on the hexagonal element in order to improve the trade-off between computational cost and accuracy, in particular for multiphysics simulations where, often, thermalhydraulic modelling requires only assembly-average cross-sections to be defined (e.g. severe accident of fast breeder reactors) i.e. the assemblies are assumed homogeneous. One approach to achieve this goal is through the use of generalised barycentric functions such as the Wachspress rational functions. This research endeavour deals with the application of Wachspress rational functions to the neutron transport equation for hexagonal geometries up to order 3. With this method, it is possible to decrease the number of spatial unknowns required for the same accuracy, and thus the computational burden for complex geometries, such as honeycomb lattices is reduced.