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阴阳网格守恒算法的设计和改进

刘洁 彭新东

刘洁, 彭新东. 阴阳网格守恒算法的设计和改进[J]. 大气科学, 2017, 41(5): 1076-1086. doi: 10.3878/j.issn.1006-9895.1703.16262
引用本文: 刘洁, 彭新东. 阴阳网格守恒算法的设计和改进[J]. 大气科学, 2017, 41(5): 1076-1086. doi: 10.3878/j.issn.1006-9895.1703.16262
Jie LIU, Xindong PENG. Design and Improvement of the Conservative Constraint Algorithm on the Yin-Yang Grid[J]. Chinese Journal of Atmospheric Sciences, 2017, 41(5): 1076-1086. doi: 10.3878/j.issn.1006-9895.1703.16262
Citation: Jie LIU, Xindong PENG. Design and Improvement of the Conservative Constraint Algorithm on the Yin-Yang Grid[J]. Chinese Journal of Atmospheric Sciences, 2017, 41(5): 1076-1086. doi: 10.3878/j.issn.1006-9895.1703.16262

阴阳网格守恒算法的设计和改进

doi: 10.3878/j.issn.1006-9895.1703.16262
基金项目: 

国家自然科学基金项目 41575103

国家自然科学基金项目 41175095

国家十二五科技支撑计划项目 2012BAC22B01

详细信息
    作者简介:

    刘洁, 女, 1991年出生, 硕士研究生, 主要从事大气数值模式与模拟的研究。E-mail:liujie00821@163.com

    通讯作者:

    彭新东, E-mail:pengxd@camscma.cn

  • 中图分类号: P456

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

Funds: 

National Natural Science Foundation of China 41575103

National Natural Science Foundation of China 41175095

National Science and Technology Pillar Program during the Twelfth Five-Year Plan Period 2012BAC22B01

  • 摘要: 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。
  • 图  1  阴阳网格构造示意图:(a)阴网格;(b)阳网格;(c)阴阳网格

    Figure  1.  Schematic diagram of the Yin–Yang grid: (a) Yin grid; (b) Yang grid; (c) Yin–Yang grid

    图  2  阴阳网格质量、通量重构计算示意图。虚线:阴网格;实线:阳网格

    Figure  2.  The schema of quality and flux reconstruction on Yin (dashed lines) and Yang (solid lines) grids

    图  3  α=0°时,MFL方案“余弦钟”平流12 d标量场的分布(等值线从0.1到0.9,间隔是0.1),平流顺序为c(实线)→d→e→f→g→c(虚线),点线为阴阳网格的分界线(下同)

    Figure  3.  The distribution of a scalar quantity of "cosine bell" during 12-day advection with MFL scheme (a mass-conservative algorithm of cell-wise bi-linear mass distribution and piece-wise linear flux distribution over the boundary) at α=0°. The contours are plotted from 0.1 to 0.9 with an interval of 0.1, the bell rotates in an order from c (solid lines)→d→e→f→g→c (dashed lines). The dotted line shows the boundary of the Yin and Yang grids, the same hereafter

    图  4  α=0°时,(a)MFC方案和(b)MFL方案计算“余弦钟”平流的全球积分总质量(左轴)和标准化误差(L1L2Linf,右轴)随时间变化,(c)MFC方案与MFL方案的L1之差△L1(左轴)和△L1/L1(右轴)随时间变化,(d)MFC方案与MFL方案的L2之差△L2(左轴)和△L2/L2(右轴)随时间变化

    Figure  4.  Temporal evolutions of global mass integration (left axis) and the normalized errors (L1, L2, Linf, right axis) of "cosine bell" advection with schemes (a) MFC (a mass-conservative algorithm of cell-wise constant mass distribution and piece-wise constant flux distribution over the boundary) and (b) MFL at α=0°, (c) temporal evolutions of △L1 (the difference between L1 of MFC scheme and L1 of MFL scheme, left axis) and △L1/L1 (right axis), (d)△L2 (the difference between L2 of MFC scheme and L2 of MFL scheme, left axis) and △L2/L2 (right axis) at α=0°

    图  5  图 4,但为α=90°

    Figure  5.  As in Fig. 4, but for α=90°

    图  6  α=45°时,(a)MFC方案和(b)MFL方案计算正弦波试验的全球积分总质量(左轴)和标准化误差(L1L2Linf,右轴)随时间变化,(c)MFC方案与MFL方案的L1之差△L1(左轴)和△L1/L1(右轴)随时间变化,(d)MFC方案与MFL方案的L2之差△L2(左轴)和△L2/L2(右轴)随时间变化

    Figure  6.  Temporal evolutions of global mass integration (left axis) and normalized errors (L1, L2, Linf, right axis) in sine wave test with schemes (a) MFC and (b) MFL at α=45°, (c) temporal evolutions of △L1 (left axis) and △L1/L1 (right axis), (d)△L2 (left axis) and △L2/L2 (right axis) at α=45°

    图  7  图 6,但为α=90°

    Figure  7.  As in Fig. 6, but for α=90°

    图  8  MFL方案变形流试验(a)初始场、(b)积分10步、(c)积分20步和(d)积分32步的高度场(阴影)分布,等值线(等值线从−0.05到0.05,间隔是0.02)代表数值解与解析解的差值

    Figure  8.  Height field in the deformational flow test with MFL scheme: (a) Initial condition, and integration after (b) 10, (c) 20, and (d) 32 steps (shaded areas). The contours (contours from −0.05 to 0.05 with an interval of 0.02) show differences between the numerical and analytical solutions

    图  9  (a)MFC方案和(b)MFL方案在变形流试验中的全球积分总质量(左轴)和标准化误差(L1L2Linf,右轴)随时间变化;(c)MFC方案与MFL方案的误差之差△L1(左轴)和△L1/L1(右轴)随时间变化,(d)MFC方案与MFL方案的误差之差△L2(左轴)和△L2/L2(右轴)随时间变化

    Figure  9.  Temporal evolutions of global mass integration (left axis) and normalized errors (L1, L2, Linf, right axis) in deformational flow test with schemes (a) MFC and (b) MFL, (c) temporal evolutions of △L1 (left axis) and △L1/L1 (right axis), and (d)△L2 (left axis) and △L2/L2 (right axis)

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出版历程
  • 收稿日期:  2016-11-08
  • 网络出版日期:  2017-03-22
  • 刊出日期:  2017-09-15

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