A quasi-diffusion method for unstructured quadrilateral meshes in 2d XY geometry

In this paper we present the quasi-diffusion (QD) method for solving the transport equation in Cartesian XY geometry on multi-level spatial meshes of arbitrary quadrilaterals. For the low-order quasi-diffusion (LOQD) equations, we propose a second-order finite difference discretization. For the transport equation, we use a conservative short characteristics method with linear approximation of the scattering source term and parabolic representation of the angular flux on incoming faces. We analyze numerical convergence of the LOQD and transport discretizations individually using tests with manufactured solutions. We then present numerical test results for the QD discretization. (authors)