自由液面與渦流流場之研究(3/3)
Date Issued
2004
Date
2004
Author(s)
DOI
922611E002021
Abstract
The mail purpose of the present study aims at the establishment of a numerical
model for a nonlinear 3D free surface flows with the emphasis on the vortical
structure. In order to comprehend the motion of the fluid flows, the Navier-Stokes
equations through the velocity-vorticity formulation are adopted to deal with free
surface flows. The governing equations for the velocity field are deduced to the linear
Poisson equations which will be solved by the finite element method (FEM). The
governing equations of vorticity field are the vorticity transport equations. As far as
solution of vorticity is concerned, we have successfully developed a finite element
method (FEM) model to attack the advection-diffusion-reaction equation. In the
free-surface boundary conditions, the kinematic boundary conditions are imposed on
the free surface positions, while the velocity on the free surfaces is solved by using
the free surface dynamic boundary conditions. While analyzing a three-dimensional
problem, there are a lot of data to be handled during the calculating process. Although
the calculating power of computer is now advancing, it still costs a lot of time to
compute. In order to increase the efficiency of computation, the present research work
will investigate parallel computation techniques for finite element analysis. It is more
important to discuss that the motion of incompressible flows with free surface flows
are solved by the finite element method using Velocity-Vorticity formulation. In
tradition, the most investigators solve free surface floe problems using primitive
variable methods or vorticity-stream function method, so it is very difficult to attempt
the velocity-vorticity formulation in dealing with the fluid dynamics with free surface
flows.
The project will be carried out for 3 years. The first year will concentrate the
establishment of the models for two dimensional free surface flows. To verify the
numerical model, the present study naturally gives more reasonable results on
problems including the maximum run-up of a solitary wave reflected from the vertical
and obliquity walls, the propagation of water waves over a block. In the second year,
comparison between the 2D and 3D models for water waves over a block will be
undertaken. In the third year, the density stratification of free surface flows and
rotational effects will be modeled. The models will be calibrated and verified by using
the laboratory or the field data. The development of these nonlinear free surface flow
models will provide a predictive tool for the design guidance for practical engineers in
the water pollutant control of the deteriorated environments of Taiwan coastal and
river waters.
Subjects
Free surfaces
Vortical flows
Velocity-Vorticity formulation
Finite element methods
Parallel computation
SDGs
Publisher
臺北市：國立臺灣大學土木工程學系暨研究所
Type
report
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