Adaptive refinement for PN neutron transport equation based on conjoint variational formulation and discontinuous finite element method

A family of variational principles based on discontinuous finite element for solving the transport equation is considered. Furthermore in this paper the adaptive h-refinement approach based on conjoint variational formulation has been presented. The conjoint maximum principle derived, not only ensures global particle conservation for the whole system but also a local neutron balance for every element and every moment of directional. The spatial dependence of the even-parity and odd-parity angular flux has been modeled using discontinuous finite element method. The efficacy of the method is assessed by comparing the number of required meshes which is necessary using continuous finite element method to indicate what savings can be achieved by discontinuous finite element strategy. In order to calculate the average element flux by this method, a new computing code, DISFENT, has been developed which has capability to solve neutron transport equation in 2D geometry. Coarser meshes efficiency tested along with several well-known neutron transport problems and the numerical results are presented to confirm theoretical results and demonstrate the performance of the proposed method while is coupled with adaptive refinement.