Spatially Continuous Mixed Simplified P2-P1 Solutions for Multidimensional Geometries

The simplified PN (SPN) angular approximation to the neutron transport equation has received renewed interest in recent years [1-3]. The even-order simplified P2 angular approximation has been shown to yield improved accuracy over the P1 (diffusion) angular approximation for problems in which the P1 approximation is reasonably accurate [1]. In particular, integral quantities such as reaction rates and eigenvalues computed by the SP2 approximation are typically more accurate. The SP2 scalar flux spatial distributions are also often more accurate than the P1 distributions away from material interfaces and source discontinuities. However, the SP2 scalar flux distributions are spatially discontinuous at material interfaces and source discontinuities. These spatial discontinuities are unphysical, aesthetically displeasing, and can lead to large inaccuracies near interfaces. Brantley [4] has recently investigated combining the P1 and P2 angular approximations in planar geometry to eliminate the discontinuities in the P2 scalar flux distributions near material interfaces and source discontinuities. In essence, the P1 angular approximation is used at material interfaces and source discontinuities to obtain spatially continuous scalar flux distributions; the P2 angular approximation is utilized elsewhere to take advantage of its improved accuracy. The combined angular approximation smoothly transitions between the P1 and P2 approximations. In this paper, we extend this planar geometry mixed P2-P1 angular approximation approach to the multidimensional SP2 angular approximation, i.e. we develop a spatially continuous mixed SP2-P1 angular approximation. We present numerical results from a two-dimensional test problem to demonstrate the accuracy of this spatially-continuous mixed SP2-P1 angular approximation