Numerical Study of Free Surface Flow and Convective Heat Transfer for 2D and 3D Problems
Date Issued
2004
Date
2004
Author(s)
Lo, Der-Chang
DOI
en-US
Abstract
The main topics of this dissertation are to apply the differential quadrature (DQ) method and finite element method (FEM) for modeling two- and three-dimensional Navier-Stokes equations in velocity-vorticity form and primitive variables.
First of all, a novel velocity-vorticity formulation is used for 2D and 3D Navier-Stokes equations and its applications in natural convection cavity flow by using DQ method. The main advantages are that the velocity and vorticity as well as temperature fields can be accurately solved by a coupled solution scheme using a single global matrix for all the unknown variables. Vorticity values are automatically determined more accurately by the use of the DQ method using much coarser meshes compared to other numerical schemes.
Secondly, a projection method based on FEM numerical procedure for solving primitive variables form of the Navier-Stokes equations in three dimensions is undertaken. The key idea is that the proposed numerical scheme involves the operator splitting technique, balance tensor diffusivity (BTD), Runge-Kutta time-stepping method, and a conjugate gradient iterative solver. The lid-driven cavity flow and laminar flow over 3D backward-facing step problems are chosen to test the feasibility and accuracy of the method. Further a mixed convection in a two-sided lid-driven differentially heated cubic cavity is investigated numerically.
Finally, the development of an innovative scheme for simulating 2D and 3D free surface flow is made using velocity-vorticity formulation. With the use of the velocity-vorticity formulation, the computations of the pressure fields in the interior regions and at the free surface of the computational domain are completely eliminated. The efficiency of the proposed numerical scheme for free surface flow is proven to be accurate from the numerical examples considered in the present work. Furthermore the advantage of this formulation with respect to primitive variables formulation is addressed from computational point of view.
Subjects
自由液面
熱傳
數值研究
free surface
heat transfer
Numerical study
Type
thesis
File(s)![Thumbnail Image]()
Loading...
Name
ntu-93-D90521004-1.pdf
Size
23.31 KB
Format
Adobe PDF
Checksum
(MD5):66e4f4b3285ad387f363c18bc22587e8