Applied Mathematics and Mechanics

, Volume 33, Issue 6, pp 687–700

# Iterative and adjusting method for computing stream function and velocity potential in limited domains and convergence analysis

• Ai-bing Li (黎爱兵)
• Li-feng Zhang (张立凤)
• Zeng-liang Zang (臧增亮)
• Yun Zhang (张 云)
Article

## Abstract

The stream function and the velocity potential can be easily computed by solving the Poisson equations in a unique way for the global domain. Because of the various assumptions for handling the boundary conditions, the solution is not unique when a limited domain is concerned. Therefore, it is very important to reduce or eliminate the effects caused by the uncertain boundary condition. In this paper, an iterative and adjusting method based on the Endlich iteration method is presented to compute the stream function and the velocity potential in limited domains. This method does not need an explicitly specifying boundary condition when used to obtain the effective solution, and it is proved to be successful in decomposing and reconstructing the horizontal wind field with very small errors. The convergence of the method depends on the relative value for the distances of grids in two different directions and the value of the adjusting factor. It is shown that applying the method in Arakawa grids and irregular domains can obtain the accurate vorticity and divergence and accurately decompose and reconstruct the original wind field. Hence, the iterative and adjusting method is accurate and reliable.

## Key words

limited domain stream function velocity potential iteration and adjustment convergence

O302 P425

## 2010 Mathematics Subject Classification

65N12 76M20 86-08

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© Shanghai University and Springer-Verlag Berlin Heidelberg 2012

## Authors and Affiliations

• Ai-bing Li (黎爱兵)
• 1
• Li-feng Zhang (张立凤)
• 1
Email author
• Zeng-liang Zang (臧增亮)
• 1
• Yun Zhang (张 云)
• 1
1. 1.Institute of MeteorologyPLA University of Science and TechnologyNanjingP. R. China