cavity
Location: http://people.sc.fsu.edu/~jburkardt/classes/math1091_2020/cavity/cavity.html
cavity,
considers some flow problems that occur in a driven cavity.
The notes:
Useful codes:
-
arrows.m,
uses the quiver() command to plot both velocity and
velocity direction fields.
-
divergence.m,
estimates the divergence of a vector field that has been
evaluated at points on a grid.
-
psi_square.m,
stream function for rotating flow in a square.
-
rms_norm.m,
returns the root-mean-square (RMS) norm of a matrix or vector.
-
uv_from_psi.m,
estimate velocities from a table of stream function values.
-
uv_square.m,
velocities for rotating flow in a square.
-
xy_square.m,
node coordinates for rotating flow in a square.
Skeletons: These are starting codes for the corresponding exercises
and the homework.
In each case, there is some missing text that you need to fill in.
Exercises: Look at these after you have tried to do the
work on your own, using the skeleton codes.
-
exercise1.m,
verifies that psi_square() generates the uv_square velocities.
-
exercise2.m,
for the rotating flow in the square, computes the velocity
field directly and indirectly, and compares the norms of
the divergence.
-
exercise3.m,
for the rotating flow in the square, add a temperature field,
and use a version of the advection equation to move a blob of
hot water around the region.
-
exercise3.png,
a plot of the temperature distribution on the last time step.
-
exercise4.m,
uses the stream function and vorticity formulation to solve
for a varying rotating flow in the square, the driven cavity
problem.
-
exercise4.png,
a plot of the variables on the last time step.
Homework: My version posted after you have turned yours in.
-
hw9.m,
repeats exercise4, but now adding a temperature field,
and a blob of hot water that we hope to see swirling around.
-
hw9.png,
a plot of the variables at the last time step.
Images:
-
washer.png,
the driven cavity models rotating flow, something like what
occurs in a washing machine.
Last revised on 26 June 2020.
