advection

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

advection, considers methods for the solution of the advection equation in 1 spatial dimension, with a constant velocity field.

The notes:

• advection.pdf
• advection.tex

Useful code:

• bumpy.m, evaluates a "bumpy" traveling wave that is a solution of the advection equation.
• smoothie.m, evaluates a "smooth" traveling wave that is a solution of the advection equation.

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

• exercise1.m, "solve" the advection equation by displaying the exact solution.
• exercise2.m, solve the advection equation with the FTCS method.
• exercise2.png, a snapshot of the solution at the last time step, for the smoothie initial condition.
• exercise3.m, solve the advection equation with the upwind method.
• exercise4.m, solve the advection equation with the Lax Friedrichs method.
• exercise4.png, a snapshot of the solution at the last time step, for the smoothie initial condition.

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

• hw6.m, solve the advection equation with the Lax Wendroff method.
• hw6.png, a snapshot of the solution, at the last time step, for the bumpy initial condition.

Images:

• swept_away.png