A Multi-Moment Finite Volume Scheme for Nonhydrostatic Atmospheric Dynamics on a Hexagonal Prism Grid

To achieve strong scalability in global models and accurately simulate atmospheric flows over complex underlying surfaces, unstructured grids have attracted increasing attention due to their flexibility. However, developing high-order numerical models on these complex grids remains a major challenge. In this study, we propose a multi-moment scheme for three-dimensional nonhydrostatic atmospheric dynamics on a hexagonal prism grid. Two kinds of moments, namely the point value and the volume-integrated average, are employed to implement the spatial reconstruction using a single-cell stencil, enabling robust and accurate formulation on unstructured grids. The quadratic reconstruction polynomial is determined by a least-squares approach to minimize asymmetric errors. In the vertical direction, a conservative finite-difference method is employed within a height-based terrain-following coordinate system. Benchmark tests demonstrate that the model achieves third-order accuracy and accurately simulates complex three-dimensional atmospheric flows. The proposed scheme can be readily extended to the icosahedral-hexagonal grid to develop a global atmospheric model. Furthermore, this study establishes a unified multi-moment framework for constructing high-order atmospheric models on fully unstructured meshes.