In this paper, two modifications are introduced for improving the accuracy, versatility, and robustness of a class of hybrid methods for radiation transport. In general, such methods are constructed by splitting the radiative flux into collided and uncollided components to which low- and high-resolution angular approximations are applied, respectively. In this work we focus on discrete ordinates discretizations of high and low order. The first modification we introduce changes the way in which the collided component is mapped into the uncollided component at the end of each time step in a simulation. The new mapping is a Nyström-type reconstruction that is applicable to arbitrary discrete ordinates quadratures, is guaranteed to preserve positivity of the solution provided that all ordinate weights are positive, is significantly more accurate than previous methods, and can be readily extended to other discretizations such as moment methods, finite element methods, and diffusion approximations. The second modification leverages integral deferred correction (IDC) to iteratively correct for the splitting error introduced by the inconsistency in angular discretization between the collided and uncollided components, in addition to improving the accuracy of the low-order temporal error that is treated by traditional IDC methods. Numerical tests in one- and two-dimensional geometries are used to demonstrate the increased accuracy and efficiency of the proposed modifications. It is found that the two techniques combined yield methods with solution accuracy and memory requirements comparable to that of monolithic discrete ordinates methods while reducing runtime by as much as a factor of between two and ten, depending on the problem.

在本文中，为改进一类混合辐射传输方法的准确性，多功能性和鲁棒性，引入了两种修改方法。通常，通过将辐射通量分成分别应用了低分辨率和高分辨率角度近似的碰撞分量和非碰撞分量来构造这样的方法。在这项工作中，我们专注于高阶和低阶的离散坐标离散化。我们引入的第一个修改更改了在模拟的每个时间步结束时将碰撞分量映射到非碰撞分量的方式。新的映射是Nyström类型的重构，适用于任意离散的坐标正交，只要所有坐标权重均为正，就可以保证保持解的正性，比以前的方法精确得多，并且可以很容易地扩展到其他离散化方法，例如矩方法，有限元方法和扩散近似。第二种修改是利用积分递延校正（IDC）来迭代校正碰撞分量和非碰撞分量之间的角度离散化不一致引起的分裂误差，此外还提高了传统IDC处理的低阶时间误差的准确性方法。使用一维和二维几何形状的数值测试来证明所提出的修改的准确性和效率得到提高。