Solution of the Convection Equation Using Unstructured Grids
A 1994 NPAC REU PROJECT
Abstract:
The project investigates the use of unstructured grids to
solve problems of interest in fluid dynamics. The two-dimensional
convection equation (a first-order wave equation) is selected as a
model problem, and a finite-volume numerical formulation
is used. The calculations are first carried out for the
wave equation with constant coefficients in a square domain.
The second problem involves the tracking of material
lines in a flow over a cylinder. This fluid-dynamics problem is governed
by the wave equation
with variable coefficients. Results computed with this unstructured-grid
is compared to previous results obtained with a structured-grid method
to evaluate both numerical accuracy and computational performance.
Introduction
Many physical problems are governed by wave-propagation phenomenon.
The first-order wave equation is an important
model equation for problems in fluid dynamics. In one dimension, this
equation can be written as
This linear equation is of the hyperbolic type; it describes a wave
propagating in the 
-direction with velocity 
.
The research considers the two-dimensional wave equation
of the form
where 
and 
are the velocity components in the - and
-directions, respectively. Two test cases are examined.
In the first test case, the standard linear
wave equation is solved on a square domain, with
velocity components taken to be constant (u=v=1).
In the second test case, the
equation governing the convection of the material lines about a cylinder is
solved. In this case, the velocity components are taken
to be the potential-flow solutions about a cylinder [5].
Numerical method
Results
If you would like to see my project in detail, please click here for
my final paper .
You can click here to return to my homepage .
