基于谱元法的热毛细流模拟及线性稳定性分析.docx

基于谱元法的热毛细流模拟及线性稳定性分析.docx基于谱元法的热毛细流模拟
及线性稳定性分析
重庆大学博士学位论文
学生姓名:尹林茂
指导教师:曾忠教授
专业:流体力学
学科门类:工学
重庆大学航空航天学院
二 O 一六年四月
Thermocapillary-Flow Simulation and
Linear Stability Analysis based on Spectral
Element Method
A Thesis Submitted to Chongqing University
in Partial Fulfillment of the Requirement for the
Doctor’s Degree of Engineering
By
Linmao Yin
Supervised by Prof. Zeng Zhong
Specialty: Fluid Mechanics
College of Aerospace Engineering of Chongqing University,
Chongqing, China
April, 2016
重庆大学博士学位论文
II
英文摘要
ABSTRACT
The thermocapillary flow, driven by the non-uniform surface tension along free
surface, appears often in industrial processing. Numerical simulation on thermocapillary
flow, coupling with the dynamic deformation of free surface, is a long-term challenge in
computational fluid dynamics. Meanwhile, the investigation on thermocapillary flow
and its instability is important in many engineering application. In this paper, a Galerkin
spectral element method (GSEM) and linear stability analysis based on GSEM were
developed, and then thermocapillary flow and its instability were investigated. My main
works are summaried briefly as:
① In accordance with the spectral approximation theory of the Fourier/Legendre
orthogonal function systems, the Legendre-Legendre spectral element method and the
Fourier-Legendre spectral element method for the Poisson-type equations were
developed, then parison of putational accuracy between the two spectral
element methods (SEM) was performed.
② In solving the unsteady Navier-Stokes equations, the time splitting method
(TSM), including the classical time splitting method (CSM) and the normal time
splitting method (NSM), is widely applied in literature. In this paper, an improved TSM,
so-called the present time splitting method (PSM) was proposed. By modifying the
pressure boundary condition, the proposed PSM is superior to CSM in accuracy and
better than NSM in stability.
③ In solving the steady Navier-Stokes equat