论文标题
在立方体上，具有积极性的保守性半拉格朗日多态全球运输模型
A positivity-preserving conservative Semi-Lagrangian Multi-moment Global Transport Model on the Cubed Sphere
论文作者
论文摘要
在立方体网格上已经开发了通过多弹性有限体积方法来保存阳性的保守性半拉格朗日传输模型。在本文中，在单个单元格中定义了两种矩，即在单元格边界和集成平均值（通过）平均值（通过）平均值（VIA）值的点值（PV矩）。 PV力矩通过常规的半拉格朗日方法更新，而通过通量形式的公式施放，可以确保确切的数值保护。与CSL2（具有二阶多项式函数的保守半拉格朗日方案）中使用的空间近似不同，这是一种单调合理函数，可以有效地消除非物理振荡并保留形状，由PV矩和动力矩重建在单个单元中。最终的方案本质上是保守的，并且可以允许大于一个的CFL数字。此外，该方案仅使用一个单元进行空间重建，这对于实际实现非常容易。提出的模型通过几种广泛使用的基准测试对立方体几何形状进行评估。数值结果表明，与CSL2方案相比，提出的运输模型可以有效地消除非物理振荡并保留数值非负性，并且它具有在实际大气模型中准确地运输示踪剂的潜力。
A positivity-preserving conservative semi-Lagrangian transport model by multi-moment finite volume method has been developed on the cubed-sphere grid. In this paper, two kinds of moments, i.e. point values (PV moment) at cell boundaries and volume integrated average (VIA) value, are defined within a single cell. The PV moment is updated by a conventional semi-Lagrangian method, while the VIA moment is cast by the flux form formulation that assures the exact numerical conservation. Different from the spatial approximation used in CSL2 (conservative semi-Lagrangian scheme with second order polynomial function) scheme, a monotonic rational function which can effectively remove non-physical oscillations and preserve the shape, is reconstructed in a single cell by the PV moment and VIA moment. The resulting scheme is inherently conservative and can allow a CFL number larger than one. Moreover, the scheme uses only one cell for spatial reconstruction, which is very easy for practical implementation. The proposed model is evaluated by several widely used benchmark tests on cubed-sphere geometry. Numerical results show that the proposed transport model can effectively remove unphysical oscillations compared with the CSL2 scheme and preserve the numerical non-negativity, and it has the potential to transport the tracers accurately in real atmospheric model.
