A quasi-transport integral variational nodal method for homogeneous nodes based on the 2D/1D method

Abstract

There is a pressing need to reduce the computational costs of methods for solving neutron transport problems while maintaining these methods' accuracy. Thus, this paper presents a quasi-transport method to accelerate the integral variational nodal method (VNM) with homogeneous nodes. The even-parity neutron transport equation (NTE) is converted to a quasi-transport form using the two-dimensional/one-dimensional (2D/1D) approximation. The radial-axial cross derivatives are eliminated, and the corresponding nodal functional is derived. Response matrices (RMs) are obtained using a classical Ritz procedure. The radial and axial flux distributions within the nodes are separately approximated by orthogonal polynomials. The integral method is applied to angular approximations for rapid RM construction. Spatial discretization is achieved using orthogonal polynomials on the interfaces. In angle, the radial interfaces are treated with spherical harmonics (PN), whereas axial interfaces are approximated with diffusion. The quasi-transport integral VNM is examined using the TAKEDA-2 and TAKEDA-3 benchmark cases. With P7 approximation, this method reduces the memory and CPU time requirements by 75% and 93%, respectively. Elimination of the radial-axial cross derivatives and application of the axial diffusion approximation produces less than 1% regional flux error on the axial interfaces between different materials.