Dynamical low-rank (DLR) approximation methods have previously been developed for time-dependent radiation transport problems. One crucial drawback of DLR is that it does not conserve important quantities of the calculation, which limits the applicability of the method. Here we address this conservation issue by solving a low-order equation with closure terms computed via a high-order solution calculated with DLR. We observe that the high-order solution well approximates the closure term, and the low-order solution can be used to correct the conservation bias in the DLR evolution. We also apply the linear discontinuous Galerkin method for the spatial discretization. We then demonstrate with the numerical results that this so-called high-order/low-order (HOLO) algorithm is conservative without sacrificing computational efficiency and accuracy.

动态低秩 (DLR) 近似方法先前已被开发用于瞬态辐射传输问题。DLR 的一个关键缺点是它不保存重要的计算量，这限制了该方法的适用性。在这里，我们通过使用 DLR 计算的高阶解来求解具有闭合项的低阶方程来解决这个守恒问题。我们观察到高阶解很好地逼近了闭包项，低阶解可用于校正 DLR 演化中的保守偏差。我们还将线性不连续伽辽金方法应用于空间离散化。然后我们用数值结果证明这种所谓的高阶/低阶 (HOLO) 算法是保守的，而不会牺牲计算效率和准确性。