Asymptotic P_N-Equivalent S_N+1 Equations

Author： Morel J. E. Ragusa J. C. Adams M. L. Kanschat G.

ISSN： 0041-1450

Source： Transport Theory and Statistical Physics, Vol.42, Iss.1, 2013-01, pp. : 3-20

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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.