阴阳网格守恒算法改进研究

发布时间：2018-04-11 21:43

本文选题：阴阳网格 + 守恒强迫　；参考：《中国气象科学研究院》2017年硕士论文

【摘要】：阴阳网格是一种准均匀重叠网格,能够有效避免传统经纬度网格的极点奇异性和经线在极区辐合的问题,但是由于阴阳网格不能自然保证物理量的守恒性,因此,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。本文提出了一种改进阴阳网格守恒算法的方案,就是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、变形流试验、平衡流试验、全球过山气流试验,二维Rossby-Haurwitz波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。本研究还进一步尝试将三阶Runge-Kutta方法应用在已有的CIP-CSLR平流方案上,利用同样的理想试验对新方案的性能进行检验,表明新方案能够在保证守恒性的前提下有效提高收敛阶数。
[Abstract]:Yin-yang mesh is a kind of quasi-uniform overlapping grid, which can effectively avoid the singularity of the poles of the traditional longitude and latitude grid and the convergence of longitude in the polar region. However, the Yin-yang grid can not guarantee the conservation of physical quantities naturally.The quality conservation algorithm on Yin-Yang mesh is of great significance for the construction and application of Yin-Yang mesh in the global pattern, and is an important performance index for the long-term stable integration of the model and the guarantee of computing effect.In this paper, a scheme for improving the conservation algorithm of Yin and Yang grids is proposed, which is based on the existing forced algorithm of yin and yang grid conservation under the assumption of uniform mass distribution.A mass conservation forcing algorithm for bilinear mass distribution and boundary flux linear distribution is constructed to improve the accuracy of advection calculation and the stability of model integrals.The advection equation of flux form is solved numerically by CIP-CSLR advection scheme. The mass bilinear distribution is obtained by "cosine clock" advection test, sinusoidal wave test, deformation flow test, equilibrium flow test, global mountain flow test and two-dimensional Rossby-Haurwitz wave test.The new scheme for linear distribution of boundary flux is compared with the original scheme for uniform distribution of mass and flux. The standardization error and scalar field distribution show that the new scheme can effectively improve the computational effect of the conservation algorithm of Yin and Yang grids.And the calculation burden does not increase obviously, which has good practical value.Furthermore, the third order Runge-Kutta method is applied to the existing CIP-CSLR advection scheme, and the performance of the new scheme is tested by the same ideal experiment. It is shown that the new scheme can effectively improve the convergence order under the premise of ensuring conservation.
【学位授予单位】：中国气象科学研究院
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P456.7

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