Design and application of DG-FEM basis functions for neutron transport on 2D and 3D hexagonal meshes

Reactor design requires safety studies to ensure that the reactors will behave appropriateunder incidental or accidental situations. The safety studies often involve multiphysics simulations whereseveral branches of reactor physics are necessary to model a given phenomenon. In those situations, ithas 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 usuallyinvert 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 anumerical spatial discretisation scheme which would be more appropriate for honeycomb meshes. In ourpast research efforts, we have set up interesting discretisation schemes in the finite element setting in2D and we wish to extend them to 3D geometries which are prisms with a hexagonal base. In 3D, arigorous 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 compareand contrast the numerical results in a physical setting.