LI Ai-bing, ZHANG Li-feng, ZANG Zeng-liang, ZHANG Yun. Iterative and Adjusting Method for Computing Stream Function and Velocity Potential in Limited Domains and Its Convergence Analysis[J]. Applied Mathematics and Mechanics, 2012, 33(6): 651-662. doi: 10.3879/j.issn.1000-0887.2012.06.002
 Citation: LI Ai-bing, ZHANG Li-feng, ZANG Zeng-liang, ZHANG Yun. Iterative and Adjusting Method for Computing Stream Function and Velocity Potential in Limited Domains and Its Convergence Analysis[J]. Applied Mathematics and Mechanics, 2012, 33(6): 651-662.

# Iterative and Adjusting Method for Computing Stream Function and Velocity Potential in Limited Domains and Its Convergence Analysis

##### doi: 10.3879/j.issn.1000-0887.2012.06.002
• Received Date: 2011-09-26
• Rev Recd Date: 2012-03-01
• Publish Date: 2012-06-15
• Stream function and velocity potential can be easily computed by solving Poisson equations in a unique way for the global domain. Because of various assumptions for handling boundary conditions, the solution is not unique when a limited domain is concerned. So, it is very important to reduce or eliminate the effects caused by uncertain boundary condition. An iterative and adjusting method based on the Endlich iteration method was presented to compute stream function and velocity potential for limited domains. This method did not need an explicitly specifying the boundary condition, while it could obtain the effective solution and was proved to be successful in decomposing and reconstructing the horizontal wind field with very small errors. The convergence of the method depended on relative value between the distances of grid in two different directions and was related to the value of the adjusting factor. Applying the method in Arakawa grids and irregular domains, the results showed that it could not only obtain accurate vorticity and divergence, but also accurately decompose and reconstruct the original wind field. Hence, the iterative and adjusting method was accurate and reliable.
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沈阳化工大学材料科学与工程学院 沈阳 110142

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