Development of micro-meso scale atmospheric environmental simulator with CIP finite volume method

高性能的数值模式在评估和预测地球大气中的自然灾害和环境危害方面发挥着至关重要的作用。在本研究项目下，我们对建立高精度、高效率和高鲁棒性的大气动力学数值模式的关键问题进行了一些基础性研究。本文的主要工作如下：1）在CIP/多矩有限体积框架下，提出了一种统一的可压缩和不可压缩流动的数值方法。该模型消除了马赫数从零到无穷大范围内的所有奇异性，具有严格的数值守恒性。2）设计了一种基于多矩概念的新网格，称为“M-网格”。理论分析和数值实验表明，在所有网格分辨率下，M型网格都具有比Arakawa型有限差分网格更好的数值频散。3）建立了直接模拟微尺度气水相互作用的数值模型。空气/水界面的明确解决了界面捕获方法，我们最近开发的。数值模型在Earth Simulator等超级计算机平台上进行了并行化和优化。4）针对地形的几何复杂性，发展了非结构网格上的数值计算方法。5<th>）在球面几何和整体模型的实现方面，我们采用了阴阳网格、球心立方网格和二十面体网格三种新型的整体网格，建立了几种高精度的数值计算公式。阴阳网格的完全保守性是通过在重叠边界上加入通量修正而得到的。所有原型模型在不同的球形网格进行了验证与数值基准测试，发现有前途的。

High performance numerical models play an essential role in accessing and predicting natural disasters and environmental hazards in earth's atmosphere. We, under this research project, carried out some fundamental studies concerning the key issues in constructing numerical models for atmospheric dynamics with high accuracy, efficiency and robustness. Our major achievements are as follows.1)We have proposed a unified numerical procedure for both compressible and incompressible flows using the CIP/multi-moment finite volume framework. The model eliminates all the singularities for Mach number ranging from zero to infinite and possesses rigorously the numerical conservativeness.2) A new grid based on the multi-moment concept, so called "M-grid", has been devised. Theoretical analysis and numerical experiments show that the M-grid has better numerical dispersion than any Arakawa-type finite difference grid for all grid resolutions.3)We have built a numerical model for direct simulation of the interactions between air and water of micro-scale flows. The air/water interface is explicitly resolved by an interface capturing method we developed recently. The numerical model has been parallelized and tuned on Earth Simulator and other supercomputer platforms.4)The numerical formulations on unstructured meshes have been developed to deal with the geometrical complexity in topography. We obtained 4^<th>-order accuracy on triangular unstructured mesh.5)Toward the implementation in the spherical geometry and the global model, we have constructed several accurate and robust numerical formulations using three new-type global grids, i.e. the Yin-Yang grid, the gnomonic cubic grid and the icosahedral grid. The complete conservativeness of the Yin-Yang grid was obtained by including a flux modification across the overset boundaries. All prototype models on different spherical grids are verified with numerical benchmark tests and found promising.