A new indirect measure of diffusion model error

- We define a diffusion model error source that is generated with a transport solution.
- When this source is added to the diffusion equation, a transport solution is obtained.
- The efficacy of this source is numerically demonstrated for a Marshak-wave problem.

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 angle-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. This source can be interpreted as the residual obtained by inserting the transport solution for the angle-integrated intensity into the diffusion equation. Perhaps the most well-known indirect measure of the diffusion model error is the 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 for the radiation transport equations with linear-discontinuous Galerkin spatial discretization and Sn angular discretization. This numerical source is computationally tested and shown to reproduce the transport solution for a Marshak-wave problem when added to the diffusion equation written in first-order or P1 form and discretized in a manner consistent with the transport equations.