| dc.description.abstract | Numerical methods are often used to approximate the solutions to partial differential equations.
Each problem may warrant the use of multiple numerical methods to solve for each domain over
which the problem is posed. For the form of the neutron transport equation developed in this work, a discontinuous finite element method (DFEM) is utilized to discretize and solve the transport problem over physical space. Furthermore, the level of spatial refinement implemented with the DFEM influences both the accuracy of the solution and the time needed to solve the problem. This work serves to extend the existing Linear Discontinuous (LD) finite element method in Texas A&M University’s parallel deterministic transport code PDT to an axially quadratic DFEM deemed Linear Discontinuous Quadratic-in-Z (LDQZ) in the hope of both increasing the accuracy of the solution provided by the existing DFEM and reducing the time needed to arrive at the solution. This increase in performance is investigated on a neutronics slab problem, a criticality slab problem, a 3D C5G7 UO₂ fuel pin, and a 3D quarter assembly from CASL’s VERA Core Physics Benchmark. For the simpler test problems modeled, the new method is shown to be more accurate via both axial flux profile comparisons and errors in the L₂ norm as well as faster for prescribed error thresholds. For the two more complex and realistic problems, LDQZ shows no significant improvement over LD when comparing axial flux and power profiles and ∆keff values while also inspecting the times to solution. | en |
