Discontinuous finite element formulations for neutron transport in spherical geometry

• We developed linear and quadratic discontinuous finite element methods in sphere.
• We found that quadratic discontinuous finite element method is the best method.
• Quadratic method has the desired convergence properties.
• Smallest L2 error norms are obtained in scalar fluxes if quadratic method is used.

We have developed the linear and quadratic Galerkin discontinuous finite element methods for the solution of both time-independent and time-dependent spherical geometry neutron transport problems. Discrete ordinates method is used for the angular discretization while the implicit method is utilized for temporal discretization in time-dependent problems. In order to assess the relative performance of the newly developed linear and quadratic discontinuous finite element spatial differencing methods relative to the previously developed linear discontinuous finite element and diamond difference discretizations, a computer code is developed and numerical solutions of the neutron transport equation for some benchmark problems are obtained. These numerical applications reveal that the newly developed quadratic discontinuous finite element method produces the most accurate results while the newly developed linear discontinuous finite element method follows as the second best discontinuous finite element method.