A third-order numerical scheme was developed for 2D irregular hexagonal meshes for the advection problems in this study. The scheme is based on a multi-moment constrained finite-volume method (MCV) in Cartesian coordinates and entails the introduction of a general integration method over a hexagonal cell. Unlike in the conventional finite-volume method, various discrete moments, that is, point value and volume-integrated average, are adopted as computational constraints to achieve high-order computation. The high-order spatial reconstruction can therefore be built in a local space, which considerably reduces the stencil length. The numerical scheme is tested using various idealized experiments. Compared with the existing schemes, this scheme is demonstrated to be flexible for application in irregular hexagonal meshes without increasing cost or compromising on accuracy. The general integration formulation based on a third-order polynomial helps to expand the application to arbitrary hexagons that does not require the use of centroids as computational points or Voronoi tessellation. It is also convenient to define the orthogonal wind components in the Cartesian system to directly drive the atmospheric transport.

针对本研究中的对流问题，针对二维不规则六边形网格开发了三阶数值方案。该方案基于笛卡尔坐标系中的多矩约束有限体积方法（MCV），并且需要在六边形单元上引入通用积分方法。与常规的有限体积方法不同，采用各种离散矩（即点值和体积积分平均值）作为计算约束，以实现高阶计算。因此，可以在局部空间中构建高阶空间重构，这大大减少了模板长度。使用各种理想实验对数值方案进行了测试。与现有方案相比，实践证明，该方案可灵活应用于不规则六边形网格，而不会增加成本或降低精度。基于三阶多项式的通用积分公式有助于将应用程序扩展到不需要使用质心作为计算点或Voronoi细分的任意六边形。在直角坐标系中定义正交风分量以直接驱动大气传输也很方便。