Abstract The Simplified ( ) 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 approximation and employ transport solutions (with high order) as reference transport solutions. Because the solution does not contain the full angular information of the transport solution, an angular intensity must be reconstructed from the solution in order to compute the 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.

中文翻译：

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简化的 PN 辐射传输方程的模型误差估计

摘要 简化的 ( ) 近似常用于模拟辐射输运现象，但它仅在一维平板几何中收敛到输运方程的真解。在所有其他几何图形中，它会导致需要量化的模型错误。在本文中，我们估计由于近似引起的辐射输运模型误差，并采用输运解决方案（高阶）作为参考输运解决方案。由于解不包含输运解的完整角度信息，因此必须从解中重建角度强度以计算模型误差。我们提出了两种这样的重建方案。模型误差估计是针对各种感兴趣的量给出的，即标量辐射强度、辐射通量和边界泄漏。提出了一种基于伴随的方法来评估模型误差，并与前向和残差技术进行比较。提出了二维数值实验。