The performance of filtered leapfrog schemes in benchmark simulations
The performance of filtered leapfrog schemes in benchmark simulations
复制标题
基准模拟中过滤蛙跳方案的性能
DOI：
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发表时间：
2021
影响因子：
8.9
通讯作者：
K. M. Kanak
中科院分区：
文献类型：
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作者：
P. Williams;J. Straka;K. M. Kanak
Robert-Asselin滤波器提供的蛙跳时间步进方案的稳定性使数十年的大气和海洋研究以及天气和气候预测成为可能。不幸的是，伴随着滤波器造成的从二阶精度到一阶精度的降低，最近迎来了新一代的蛙跳时间滤波器，其保持了二阶精度，包括Robert-Asselin-威廉姆斯（RAW）滤波器及其变体。这些现代的过滤蛙跳方案以前已被证明可以改善使用简单的概念模型和综合大气环流模型的数值模拟。然而，它们在标准基准实验中的表现以前没有被评估过。在这里，我们在四个经典的基准实验中评估这些过滤蛙跳方案：线性标量平流;准可压缩方程中的非线性密度流;完全可压缩方程中的非线性上升暖泡;以及旋转浅水方程中的非线性孪生热带气旋的关联行为。对于给定的时间步长，滤波蛙跳格式被发现与三阶Runge-Kutta（RK 3）格式相比毫不逊色。它们的计算成本也比RK 3低，每个时间步的成本大约是RK 3的三分之一到二分之一。对于一个给定的计算支出，过滤蛙跳计划被发现产生更小的误差，相对于解析解（在可用的情况下）比RK 3。此外，滤波蛙跳格式被发现是数值稳定的，即使当离散化方法从快速声波和重力波模式中分离出缓慢的平流和扩散模式时。鉴于实施过滤器升级只需要微创的变化，现有的计算机代码，我们的研究结果提供了支持，继续使用过滤蛙跳计划在大气和海洋模型。
The stabilisation of the leapfrog time‐stepping scheme provided by the Robert–Asselin filter has enabled decades of atmospheric and oceanic research and weather and climate predictions. The unfortunate concomitant reduction from second‐order accuracy to first‐order accuracy inflicted by the filter has recently ushered in a new generation of leapfrog time filters that preserve the second‐order accuracy, including the Robert–Asselin–Williams (RAW) filter and its variants. These modern filtered leapfrog schemes have previously been shown to improve numerical simulations made using both simple conceptual models and comprehensive general circulation models. However, their performance in standard benchmark experiments has not previously been assessed. Here we evaluate these filtered leapfrog schemes in four classic benchmark experiments: linear scalar advection; a nonlinear density current in the quasi‐compressible equations; a nonlinear rising warm bubble in the fully compressible equations; and the linked behaviour of nonlinear twin tropical cyclones in the rotating shallow‐water equations. For a given time‐step size, the filtered leapfrog schemes are found to compare favourably with the third‐order Runge–Kutta (RK3) scheme. They are also less computationally expensive than RK3, at roughly one‐third to one‐half the cost per time step. For a given computational expenditure, the filtered leapfrog schemes are found to produce smaller errors with respect to the analytical solution (where available) than RK3. Furthermore, the filtered leapfrog schemes are found to be numerically stable, even when the discretisation method splits the slow advection and diffusion modes from the fast acoustic and gravity‐wave modes. Given that implementing filter upgrades requires only minimally invasive changes to an existing computer code, our results provide support for the continued use of filtered leapfrog schemes in atmosphere and ocean models.