Asymptotic P N -Equivalent S N+1 Equations

Abstract

The 1-D one-speed slab-geometry P N equations with isotropic scattering can be modified via an alternative moment closure to preserve the two asymptotic eigenmodes associated with the transport equation. Pomraning referred to these equations as the asymptotic P N equations. It is well-known that the 1-D slab-geometry S N+1 equations with Gauss quadrature are equivalent to the standard P N equations. In this article, we first show that if any quadrature set meets a certain criterion, the corresponding S N+1 equations will be equivalent to a set of P N equations with a quadrature-dependent closure. We then derive a particular family of quadrature sets that make the S N+1 equations equivalent to the asymptotic P N equations. Next we theoretically demonstrate several of the properties of these sets, relate them to an existing family of quadratures, numerically generate several example quadrature sets, and give numerical results that confirm several of their theoretically predicted properties.