Asymptotic P N -Equivalent S N+1 Equations
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The 1-D one-speed slab-geometry PNequations 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 PNequations. It is well-known that the 1-D slab-geometry SN+1equations with Gauss quadrature are equivalent to the standard PNequations. In this article, we first show that if any quadrature set meets a certain criterion, the corresponding SN+1equations will be equivalent to a set of PNequations with a quadrature-dependent closure. We then derive a particular family of quadrature sets that make the SN+1equations equivalent to the asymptotic PNequations. 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. © 2013 Copyright Taylor and Francis Group, LLC.
author list (cited authors)
Morel, J. E., Ragusa, J. C., Adams, M. L., & Kanschat, G.