论文标题
用于保存时间依赖的低阶低级运输计算的高阶 /低阶（HOLO）算法
A high-order / low-order (HOLO) algorithm for preserving conservation in time-dependent low-rank transport calculations
论文作者
论文摘要
先前已经为时间依赖性的辐射传输问题开发了动力学低级别（DLR）近似方法。 DLR的一个至关重要的缺点是，它不能保留重要数量的计算，这限制了该方法的适用性。在这里，我们通过解决通过使用DLR计算的高阶解决方案计算的闭合项的低阶方程来解决此保护问题。我们观察到高阶解井接近闭合项，并且低阶解可以用于纠正DLR演化中的保护偏置。我们还应用线性不连续的盖金方法进行空间离散化以获得渐近极限。然后，我们以数值结果证明了这种所谓的高阶 /低阶（Holo）算法是保守的，而无需牺牲计算效率和准确性。
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 to obtain the asymptotic limit. 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.
