An improved variational nodal method for the solution of the three-dimensional steady-state multi-group neutron transport equation

An improved variational nodal method is presented for the solution of the three-dimensional (3D) steady-state multi-group neutron transport equation. The variational functional is constructed that reproduces the even parity neutron transport equation with isotropic scattering. 3D orthogonal polynomials are used to approximate the spatial flux distribution within the nodes and across the nodal interfaces. The angular discretization utilizes a 3D even-parity integral method within the nodes, and standard spherical harmonics (PN) on the interfaces. The generalized partitioned matrix (GPM) acceleration is derived and performed to speed up outer iterations of the transport formulation. Examined against three sets of TAKEDA benchmark cases, the integral method exhibits superior accuracy and efficiency than the standard VNM approach. In addition, the GPM method presents remarkable acceleration to outer iterations when tested on the 3D PWR problem. The joint employment of the GPM method and the PM method yields a gain of over 20 in the response matrix solution time.