Design and Application of DG-FEM Basis Functions for Neutron Transport on Two-Dimensional and Three-Dimensional Hexagonal Meshes

Abstract

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.

Keywords

• neutron transport
• discrete ordinates
• discontinuous Galerkin
• polygonal finite element
• high-order discretisation
• Wachspress functions