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Approximate analytical solutions for Kolmogorov’s equations

✍ Scribed by Tianzhi Yang; Bo Fang; Xingyuan Wang; Wenhu Huang

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
396 KB
Volume
235
Category
Article
ISSN
0377-0427

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✦ Synopsis

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.

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Approximate solution of the Fokker-Planc
Approximate solution of the Fokker-Planck-Kolmogorov equation by finite elements
✍ El-Gebeily, Mohamed A. ;Shabaik, Hosam E. Emara 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 417 KB

## Abstract The paper considers the solution of the Fokker‐Planck‐Kolmogorov equation by the finite element method (FEM). The problem is set in a variational formulation suitable for the FEM. Some theoretical aspects related to applying the method are discussed. Discretization of the problem is car