在非線性EHD動力系統內的分岔研究

Abstract

本論文是利用對流-擴散-反應的數值方法模擬于二維電液動非線性動力系統內的分岔行為。此一包含了受空間電荷密度影響的外加電場之Poisson方程式、由庫倫力所驅動的不可壓縮Navier-Stokes方程、以及可描述流場中帶電離子分佈的電荷守恆方程式。 本研究係在兩電極板中間以單極注入之方式造成非線性動力行為的分岔，它包括了對稱性分岔、倍頻率分岔、週期分岔、及最後所發展至渾沌狀態。吾人將利用模擬之結果說明其各個現象所代表的物理意義;並透過數值分析來了解電液動的分岔行為。

This study is aimed to simulate the bifurcation behavior occurring in a two-dimensional electrical hydrodynamic nonlinear dynamical system by using the convection-diffusion-reaction (CDR) numerical method. This nonlinear system includes the Poisson equation for the external electric field that is subject to the space charge density, incompressible Navier-Stokes equations driven by the Coulomb force, continuity equation, and the charge conservation equation which describes ions distribution in the hydrodynamic field. The dynamics in the investigated nonlinear system include the pitchfork-bifurcation, frequency-doubling, Hopf-bifurcation, and the chaotic dynamics. The simulation results are presented for the case of unipolar injection between two plane electrodes. Finally, we will use the numerical analysis to understand bifurcation behavior in the electrohydrodynamic.