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January  2010, 13(1): 101-116. doi: 10.3934/dcdsb.2010.13.101

Numerical simulation and self-similar analysis of singular solutions of Prandtl equations

Qiaolin He 1,

1. 

Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China

Received  May 2009 Revised  September 2009 Published  October 2009

We use the iterative grid redistribution method(IGR) to solve Prandtl equations and study the self-similar behavior of the singular solutions of them. The IGR method enables us to get more accurate solutions of Prandtl equations when they develop singularity. We also study the self-similar behavior of the singular solutions. Blow up rate and blow up profiles are derived and the results are verified by the numerical solutions.
Keywords: Prandtl equations, singularity, self-similarity..
Mathematics Subject Classification: Primary: 35Q30, 14E15; Secondary: 60G18, 33F0.
Citation: Qiaolin He. Numerical simulation and self-similar analysis of singular solutions of Prandtl equations. Discrete & Continuous Dynamical Systems - B, 2010, 13 (1) : 101-116. doi: 10.3934/dcdsb.2010.13.101
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