A new indirect measure of diffusion model error
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We define a new indirect measure of the diffusion model error called the diffusion model error source. When this model error source is added to the diffusion equation, the transport solution for the angular-integrated intensity is obtained. This source represents a means by which a transport code can be used to generate information relating to the adequacy of diffusion theory for any given problem without actually solving the diffusion equation. The generation of this source does not relate in any way to acceleration of the iterative convergence of transport solutions. Perhaps the most well-known indirect measure of the diffusion model error is the variable-Eddington tensor. This tensor provides a great deal of information about the angular dependence of the angular intensity solution, but it is not always simple to interpret. In contrast, our diffusion model error source is a scalar that is conceptually easy to understand. In addition to defining the diffusion model error source analytically, we show how to generate this source numerically relative to the Sn radiative transfer equations with linear-discontinuous spatial discretization. This numerical source is computationally tested and shown to reproduce the Sn solution for a Marshak-wave problem.
