Approximate analytical solutions for Kolmogorov’s equations

详细信息    查看全文

• 作者：Tianzhi Yang ; Bo Fang ; Xingyuan Wang ; Wenhu Huang
• 关键词：Kolmogorov’ ; s equations ; Homotopy analysis method ; Analytical solution
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2010
• 出版时间：1 December 2010
• 年：2010
• 卷：235
• 期：3
• 页码：747-755
• 全文大小：396 K

文摘

This paper reports the explicit analytical solutions for Kolmogorov’s equations. Kolmogorov’s equations are commonly used to describe the structure of local isotropic turbulence, but their exact analytical solutions have not yet been found. In this paper, the closed-form solutions for two kinds of Kolmogorov’s equations are obtained. The derivations of the approximate solutions are based on the homotopy analysis method, which is a new tool for obtaining the approximate analytical solutions of both strong and weak nonlinear differential equations. To examine the validity of the approximate solutions, numerical comparisons between results from the homotopy analysis method and the fourth-order Runge–Kutta method are carried out. It is shown that the results are in good agreement.