Global non-hydrostatic atmospheric models are becoming increasingly important for studying the climates of planets and exoplanets. However, such models suffer from computational difficulties due to the large aspect ratio between the horizontal and vertical directions. To overcome this problem, we developed a global model using a vertically-implicit-correction (VIC) scheme in which the integration time step is no longer limited by the propagation of acoustic waves in the vertical. We proved that our model, based on the $\rm Athena^{++}$ framework and its extension for planetary atmospheres - SNAP (Simulating Non-hydrostatic Atmosphere on Planets), rigorously conserves mass and energy in finite volume simulations. We found that traditional numerical stabilizers such as hyper-viscosity and divergence damping are not needed when using the VIC scheme, which greatly simplifies the numerical implementation and improves stability. We present simulation results ranging from 1D linear waves to 3D global circulations with and without the VIC scheme. These tests demonstrate that our formulation correctly tracks local turbulent motions, produces Kelvin-Helmholtz instability, and generates a super-rotating jet on hot Jupiters. Employing this VIC scheme improves the computational efficiency of global simulations by more than two orders of magnitude compared to an explicit model and facilitates the capability of simulating a wide range of planetary atmospheres both regionally and globally.

中文翻译：

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具有质量和能量守恒的垂直隐式校正 (VIC) 方案的全球非静水压大气模型

全球非流体静力大气模型对于研究行星和系外行星的气候变得越来越重要。然而，由于水平和垂直方向之间的大纵横比，此类模型存在计算困难。为了克服这个问题，我们使用垂直隐式校正 (VIC) 方案开发了一个全局模型，其中积分时间步长不再受垂直声波传播的限制。我们证明了我们的模型基于 $\rm Athena^{++}$ 框架及其对行星大气的扩展 - SNAP（模拟行星上的非流体静力大气），在有限体积模拟中严格守恒质量和能量。我们发现使用 VIC 方案时不需要传统的数值稳定器，如超粘滞和发散阻尼，大大简化了数值实现，提高了稳定性。我们展示了从 1D 线性波到 3D 全球环流的模拟结果，有和没有 VIC 方案。这些测试表明，我们的公式正确地跟踪了局部湍流运动，产生了开尔文-亥姆霍兹不稳定性，并在热木星上产生了超级旋转的喷流。与显式模型相比，采用这种 VIC 方案将全球模拟的计算效率提高了两个数量级以上，并促进了在区域和全球范围内模拟各种行星大气的能力。这些测试表明，我们的公式正确地跟踪了局部湍流运动，产生了开尔文-亥姆霍兹不稳定性，并在热木星上产生了超级旋转的喷流。与显式模型相比，采用这种 VIC 方案将全球模拟的计算效率提高了两个数量级以上，并促进了在区域和全球范围内模拟各种行星大气的能力。这些测试表明，我们的公式正确地跟踪了局部湍流运动，产生了开尔文-亥姆霍兹不稳定性，并在热木星上产生了超级旋转的喷流。与显式模型相比，采用这种 VIC 方案将全球模拟的计算效率提高了两个数量级以上，并促进了在区域和全球范围内模拟各种行星大气的能力。