自适应网格加密代码FLASH - I的树基解算器：重力和光学深度
Tree-based solvers for adaptive mesh refinement code FLASH - I: gravity and optical depths
摘要：
我们描述了一个八叉树算法的MPI并行，自适应网格细化代码{ \sc FLASH}，它可以用来计算气体的自重，也角平均的局部光学深度，处理环境漫射辐射。该算法只将树中需要在本地执行树遍历的部分传递给不同的处理器。这种方法的优点是相对较低的存储器需求，这对于需要处理来自许多不同方向的信息的光学深度计算特别重要。此功能还支持将在后续论文中描述的基于树的一般辐射传输算法，并提供高达至少1500个核心的出色扩展。重力的边界条件可以是孤立的或周期性的，它们可以在每个方向上独立地指定，使用新开发的推广埃瓦尔德方法。通过部分地重新使用来自先前时间步的解，可以利用{ \em自适应块更新}技术来加速重力计算。与{ \sc Flash}内部多重网格重力求解器的比较表明，基于树的方法提供了一种有竞争力的替代方法，特别是对于具有孤立或混合边界条件的问题。我们评估了几个多极验收标准（MAC），并确定了一个相对简单的APE MAC，它提供了高精度，低计算成本。发现光学深度估计与{ \sc RADMC-3D}辐射输运代码非常一致，树求解器快得多。我们的算法在4.0版及更高版本的{ \sc FLASH}代码的标准发行版中提供。
英文摘要：
We describe an OctTree algorithm for the MPI-parallel, adaptive mesh-refinement code {\sc FLASH}, which can be used to calculate the gas self-gravity, and also the angle-averaged local optical depth, for treating ambient diffuse radiation. The algorithm communicates to the different processors only those parts of the tree that are needed to perform the tree walk locally. The advantage of this approach is a relatively low memory requirement, important in particular for the optical depth calculation, which needs to process information from many different directions. This feature also enables a general tree-based radiation transport algorithm that will be described in a subsequent paper, and delivers excellent scaling up to at least 1500 cores. Boundary conditions for gravity can be either isolated or periodic, and they can be specified in each direction independently, using a newly developed generalisation of the Ewald method. The gravity calculation can be accelerated with the {\em adaptive block update} technique by partially re-using the solution from the previous time-step. Comparison with the {\sc Flash} internal multi-grid gravity solver shows that tree based methods provide a competitive alternative, particularly for problems with isolated or mixed boundary conditions. We evaluate several multipole acceptance criteria (MACs) and identify a relatively simple APE MAC which provides high accuracy at low computational cost. The optical depth estimates are found to agree very well with those of the {\sc RADMC-3D} radiation transport code, with the tree solver being much faster. Our algorithm is available in the standard release of the {\sc FLASH} code in version 4.0 and later.
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