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

高性能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起着至关重要的作用。在这一研究项目下，我们对建立高精度、高效率、高稳健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。本文的主要成果如下：1)提出了一种基于CIP/多矩有限体积框架的可压缩流动和不可压缩流动的统一数值方法。该模型消除了马赫数在0到无穷大范围内的所有奇异性，并具有严格的数值守恒性。2)基于多矩概念设计了一种新的网格，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网格比任何Arakawa类型的有限差分网格都具有更好的数值色散。3)建立了直接模拟微尺度气流与水相互作用的数值模型。通过我们最近开发的界面捕捉方法显式地解析了空气/水界面。数值模型已经在地球模拟器等超级计算机平台上进行了并行化和调谐。4)针对地形几何的复杂性，发展了非结构网格上的数值格式。5)针对球面网格和全球模型的实现，我们使用了三种新型的全球网格，即阴阳网格、三次网格和二十面体网格，构造了几种高精度和健壮的数值格式。阴阳网格的完全守恒性是通过包含跨越重叠边界的通量修正来获得的。所有的原型模型在不同的球面网格上都得到了数值基准试验的验证，并被认为是有前途的。

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.