An Efficient Second-Order Discontinuous Finite Volume Element Scheme for the Three-Dimensional Neutron Transport Equations

The numerical solution of the three-dimensional discrete ordinates neutron transport equations costs a lot of time on general hexahedral meshes. In this paper, we devise an efficient second-order scheme based on the discontinuous finite volume element (DFVE) method with the effective face technique, which is named the DFVE-EF scheme. The proposed scheme uses iso-parametric trilinear elements and piecewise constant spaces as the trial and test spaces, respectively. Moreover, mid-point quadrature is adopted in the discretization of surface and volume integrals. Numerical experiments are performed to validate that compared with some similar schemes such as the discontinuous finite element (DFE) scheme with 8-point Gaussian quadrature (DFE-Gauss), our DFVE-EF scheme has almost the same second-order accuracy but is more efficient on various meshes.