一种提高数值模式时间差分计算精度的新格式———回溯时间积分格式

封国林; 曹鸿兴; 谷湘潜; 丑纪范

一种提高数值模式时间差分计算精度的新格式———回溯时间积分格式

1.
扬州大学理学院物理系, 扬州 225002
2.
中国气象科学研究院, 北京 100081
3.
中国气象局培训中心, 北京100081

资助项目:

国家自然科学基金 40175024, 40175027

国家重点基础研究发展规划 G1998040901-1

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- 被引次数: 0
出版历程
- 收稿日期: 2000-02-02
- 修回日期: 2000-09-25
- 刊出日期: 2002-04-30

A NEW SCHEME FOR IMPROVING THE ACCURACY OF NUMERICAL PREDITION —RETROSPECTIVE TIME INTEGRATION SCHEME

1.
Mathematics and Physics College, Yangzhou University, Yangzhou 225009
2.
Chinese Academy of Meteorological Sciences, Beijing 100081
3.
CMA Training Center, Beijing 100081

摘要

摘要: 为了使用以制作数值预报的微分方程中包含更多的信息量、以期提高预报准确度, 该文提出了一种基于记忆动力学的时间积分格式。以天气预报为实例, 计算表明, 平流方程的回溯时间积分格式所得的预报准确度大大高于传统的蛙跃差分格式。此方法在海洋、水文、环境、航空等应用平流方程计算的多种科学中亦是有效的。
- 差分格式;
- 记忆性;
- 数值预报;
- 平流方程
Abstract: To put more information into difference scheme of a differential equation for making an accurate prediction, a new kind of time integration scheme, known as the retrospective scheme, is proposed on the basis of the memorial dynamics. Stability criteria of the scheme of an advection equation in certain conditions are derived mathematically. The computations for the advection equation have been conducted with its retrospective scheme. It is shown that the accuracy of the scheme is much higher than that of the leapfrog difference scheme. The retrospective time integration scheme can be applied to oceanography, hydrology, environmental sciences, aviation and so on.
- Time integration;
- Memory;
- Numerical weather prediction;

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图 1 稳定区域Ⅰ与不稳定区域Ⅱ、Ⅲ

(纵坐标ωΔt, 横坐标为ε, ω是频率, ε是式 (21) 中的一个记忆参数)

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图 2 ε≥0, E=(3 +ε)²/ 4-(ωΔt)²时的稳定域 (说明同图 1)

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图 3 区域Ⅱ和Ⅲ中的稳定区域

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图 4 Ⅰ、Ⅱ和Ⅲ三个区中稳定域的合并

(Ⅱ_s和Ⅲ_s是图 3中相应部分的缩小)

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表 1 蛙跃格式 (LF) 与回溯格式 (RT) 在时间积分中的精确度的比较

参考文献(10)

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