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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
A NEW SCHEME FOR IMPROVING THE ACCURACY OF NUMERICAL PREDITION —RETROSPECTIVE TIME INTEGRATION SCHEME
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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。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.
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Key words:
- Time integration;
- Memory;
- Numerical weather prediction;
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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
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