大气流动的自适应隐式平流
Adaptively Implicit Advection for Atmospheric Flows
AI总结：
本文提出局部应用于高 Courant 数区域的自适应隐式平流方法，仅需一次线性求解器迭代，即可在多种大气网格和可压缩模型中实现长时步、稳健且守恒的平流积分。
摘要：
用于平流的隐式时间步进在 Courant 数较大的空间和时间位置局部应用，而其余通常占大多数的解则采用标准显式时间步进。这种自适应隐式平流格式有助于以较长时间步进行高效且稳健的积分，同时对总体精度影响可忽略不计，并在一般网格上实现单调性和局部守恒。该方法效率方面一个新颖且重要的特点是，每次平流求解只需要一次线性求解器迭代。本文的实现采用二阶 Runge-Kutta 隐式/显式时间步进，并结合二阶/三阶有限体积空间离散。我们在球面上的变形流平流以及大气流动的完全可压缩模型背景下演示了自适应隐式平流。示踪物以非常大的 Courant 数越过经纬度网格的极点，并使用同一算法穿过六边形网格和立方球网格。具有强局部上升气流的浮力流动模拟也受益于自适应隐式平流。稳定分层流动模拟需要将重力波和声波的隐式处理与平流稳定结合，以获得较长的稳定时间步。
英文摘要：
Implicit time-stepping for advection is applied locally in space and time where Courant numbers are large, but standard explicit time-stepping is used for the remaining solution which is typically the majority. This adaptively implicit advection scheme facilitates efficient and robust integrations with long time-steps while having negligible impact on the overall accuracy, and achieving monotonicity and local conservation on general meshes. A novel and important aspect for the efficiency of the approach is that only one linear solver iteration is needed for each advection solve. The implementation in this paper uses a second-order Runge-Kutta implicit/explicit time-stepping in combination with a second/third-order finite volume spatial discretisation. We demonstrate the adaptively implicit advection in the context of deformational flow advection on the sphere and a fully compressible model for atmospheric flows. Tracers are advected over the poles of latitude-longitude grids with very large Courant numbers and through hexagonal and cubed-sphere meshes with the same algorithm. Buoyant flow simulations with strong local updrafts also benefit from adaptively implicit advection. Stably stratified flow simulations require a stable combination of implicit treatment of gravity and acoustic waves as well as advection in order to achieve long stable time-steps.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
