Spatially Continuous Functional Expansion Tallies on Unstructured Meshes

Abstract

Functional expansion tallies (FETs) have become a popular method to generate tallies from Monte Carlo simulations which are spatially continuous, and can therefore facilitate multi-physics coupling with finite-element method (FEM) based solvers in other physics domains. There are, however, several drawbacks with traditional FETs, such as requiring a set of orthogonal basis functions defined on the geometric region of the tally. Another constraint is that at the intersection between two FET regions, the functional values will not, in general, be continuous. In this work, we propose a new type of FET which we call the Lagrange FET, that can be scored on a general unstructured mesh. In the Lagrange FET, continuity is guaranteed between elements of the mesh, and orthogonal basis functions are not required, permitting the use of standard FEM interpolation techniques. A simplified version of the Lagrange FET method which supports regular Cartesian meshes has been implemented in the Abeille Monte Carlo code, and has been demonstrated on a 1D slab reactor problem in addition to the C5G7 benchmark.

Jacob Merson

Assistant Professor of Mechanical Engineering

loves to scale multiphysics simulations onto leadership class supercomputers