A geometry preserving, conservative, mesh-to-mesh isogeometric interpolation algorithm for spatial adaptivity of the multigroup, second-order even-parity form of the neutron transport equation

Abstract

In this paper a method is presented for the application of energy-dependent spatial meshes applied to the multigroup, second-order, even-parity form of the neutron transport equation using Isogeometric Analysis (IGA). The computation of the inter-group regenerative source terms is based on conservative interpolation by Galerkin projection. The use of Non-Uniform Rational B-splines (NURBS) from the original computer-aided design (CAD) model allows for efficient implementation and calculation of the spatial projection operations while avoiding the complications of matching different geometric approximations faced by traditional finite element methods (FEM). The rate-of-convergence was verified using the method of manufactured solutions (MMS) and found to preserve the theoretical rates when interpolating between spatial meshes of different refinements. The scheme’s numerical efficiency was then studied using a series of two-energy group pincell test cases where a significant saving in the number of degrees-of-freedom can be found if the energy group with a complex variation in the solution is refined more than an energy group with a simpler solution function. Finally, the method was applied to a heterogeneous, seven-group reactor pincell where the spatial meshes for each energy group were adaptively selected for refinement. It was observed that by refining selected energy groups a reduction in the total number of degrees-of-freedom for the same total L2 error can be obtained.