High order finite difference approximations to the one-group neutron diffusion equation in 1D heterogeneous media part II: Implementation and application

Verification that a numerical method performs as intended is an integral part of code development. Semi-analytical benchmarks enable one such verification modality. Unfortunately, a semi-analytical benchmark requires some degree of analytical forethought and treats only relatively idealized cases making it of limited diagnostic value. In the first part of our investigation (Part I, in these proceedings), we established the theory of a straightforward finite difference scheme for the 1D, monoenergetic neutron diffusion equation in plane media. We also demonstrated an analytically enhanced version that leads to the analytical solution. The second part of our presentation (Part II) concerns the numerical implementation and application of the finite difference solutions of Part I. Here, we demonstrate how the numerical schemes themselves provide the semi-analytical benchmark. With the analytical solution known, we therefore have a test for accuracy of the proposed finite difference algorithms designed for high order.