Open AccessSymplectic Exact Solution for Stokes Flow in the Thin Film Coating Applications
Author(s) -
Yan Wang,
Zichen Deng,
Weipeng Hu
Publication year - 2014
Publication title -
mathematical problems in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.262
H-Index - 62
eISSN - 1026-7077
pISSN - 1024-123X
DOI - 10.1155/2014/151470
Subject(s) - symplectic geometry , eigenfunction , stokes flow , legendre polynomials , hamiltonian (control theory) , mathematics , legendre transformation , hamiltonian system , separation of variables , lagrangian , flow (mathematics) , symplectic integrator , mathematical analysis , classical mechanics , eigenvalues and eigenvectors , physics , geometry , mathematical optimization , symplectic manifold , boundary value problem , quantum mechanics
The symplectic analytical method is introduced to solve the problem of the stokes flow in the thin film coating applications. Based on the variational principle, the Lagrangian function of the stokes flow is established. By using the Legendre transformation, the dual variables of velocities and the Hamiltonian function are derived. Considering velocities and stresses as the basic variables, the equations of stokes flow problems are transformed into Hamiltonian system. The method of separation of variables and expansion of eigenfunctions are developed to solve the governing equations in Hamiltonian system, and the analytical solutions of the stokes flow are obtained. Several numerical simulations are carried out to verify the analytical solutions in the present study and discuss the effects of the driven lids of the square cavity on the dynamic behavior of the flow structure
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