阴阳网格守恒算法的设计和改进

阴阳网格上的质量守恒算法对于阴阳网格在全球模式构建和应用具有重要意义，是模式长期稳定积分和保证计算效果的重要性能指标。本研究在已有的质量均匀分布假定下阴阳网格守恒强迫算法的基础上，构建网格内质量的双线性分布和边界通量线性分布的质量守恒强迫算法，以提高阴阳网格平流计算的精度和模式积分的稳定性。运用CIP-CSLR平流方案对通量形式平流方程数值求解，分别通过"余弦钟"平流试验、正弦波试验和变形流试验对质量双线性分布、边界通量线性分布的新方案与质量和通量均匀分布的原方案进行了对比，标准化误差和标量场分布均表明新方案可有效提高阴阳网格守恒算法的计算效果，且计算负担没有明显增加，具有较好的实用价值。

Design and Improvement of the Conservative Constraint Algorithm on the Yin-Yang Grid

The mass-conservative algorithm on the Yin-Yang grid is important for the construction and application of Yin-Yang grid in global atmospheric modeling studies. It is also an important index of model performance that ensures long-term stable integration and accurate computational results. In this study, the authors propose a mass-conservative algorithm of cell-wise bi-linear mass distribution and piece-wise linear flux distribution over the boundary. Compared to the conservative constraint that defines cell-wise constant mass distribution, the new algorithm improves the accuracy of advection computation on the Yin-Yang grid and enhances the stability of model integration. The flux-form advection equation is solved by using the CIP-CSLR (Constrained Interpolation Profiles-Conservative Semi-Lagrangian with Rational function) scheme. Several idealized tests, including a solid cosine-bell advection with non-divergent flow, a global transport of a sine-wave test and a test with smooth deformational flow, are conducted to compare the impact of cell-wise bi-linear distribution with that of the cell-wise constant distribution. The normalized errors and spatial distributions of scalars all suggest that the new scheme is capable of refining the global conservation status in model application, which would effectively improve the computational results of the conservative constraint on the Yin-Yang grid without greatly increasing the computational cost.