stream

Location: http://people.sc.fsu.edu/~jburkardt/classes/math1091_2020/stream/stream.html

stream, shows how problems in incompressible fluid flow can be described in terms of the stream function.

The notes:

• stream.pdf
• stream.tex

Useful codes:

• arrows.m, uses the quiver() command to plot both velocity and velocity direction fields.
• psi_channel.m, stream function for channel flow.
• psi_corner.m, stream function for corner flow.
• psi_from_uv.m, computes the stream function from the velocity.
• psi_shear.m, stream function for shear flow.
• psi_vortex.m, stream function for vortex flow.
• uv_channel.m, velocities for channel flow.
• uv_corner.m, velocities for corner flow.
• uv_shear.m, velocities for shear flow.
• uv_vortex.m, velocities for vortex flow.
• xy_channel.m, coordinates for channel flow.
• xy_corner.m, coordinates for corner flow.
• xy_shear.m, coordinates for shear flow.
• xy_vortex.m, coordinates for vortex flow.

Skeletons: These are starting codes for the exercises and homework.

• skeleton2.m
• skeleton3.m
• skeleton4.m
• skeleton5.m
• skeleton6.m, an outline of how to do the homework.

Exercises: Look at these after you have tried to do the work on your own.

• exercise1.m, plot each of the example flow fields.
• exercise2.m, evaluate the divergence for the example flows.
• exercise3.m, determine velocity vectors by differentiating the stream function.
• exercise4.m, determine stream function by integrating the velocity vectors.
• exercise5.m, solves a fluid flow using stream function and vorticity.

Homework: My version posted after you have turned yours in.

• xy_inout.txt, the node coordinates for a 41x41 grid.
• uv_inout.txt, the corresponding velocity component values.
• hw8.m, reads the two data files, creates X, Y, U and V arrays, computes the stream function PSI, and plots it.
• hw8.png, a plot of the stream function.

Images:

• stream.png, a plot that suggests the relationship between stream lines and the velocity field in a fluid flow.