Convection of a Sine Wave
Description
The Convection Equation is where is a constant.
The solution with an initial condition of is shown along with where is a small time step. This illustrates the direction of change as the red curve will move towards the green dotted curve. In this case the short time for illustration purposes.
Activities
Vary the sliders and click the play button. Note what the red curve appears to do.
How does changing the sliders affect the curve motion?
How do you translate a general function?
A general function, can be translated along the -axis a distance by evaluating . Note at the original function parameter would be zero.
What would this suggest as a possible solution to this problem?
What happens if you substitute into the partial differential equation? Note: by the chain rule.