Model Error Estimation for the Simplified P_N Radiation Transport Equations

摘要

The Simplified P_N (SP_N) approximation is often used to model radiation transport phenomena, but it converges to the true solution of the transport equation only in one-dimensional slab geometry. In all other geometries, it incurs a model error that needs to be quantified. In this paper, we estimate the radiation transport model error due to the SP_N approximation and employ S_N transport solutions (with high S_N order) as reference transport solutions. Because the SP_N solution does not contain the full angular information of the transport solution, an angular intensity must be reconstructed from the SP_N solution in order to compute the SP_N model error. We propose two such reconstruction schemes. Model error estimates are given for various quantities of interests, i.e., scalar radiation intensity, radiation flux, and boundary leakage. An adjoint-based approach is proposed to evaluate the model error and is compared against forward and residual techniques. Two-dimensional numerical experiments are presented.