1D Linear Advection

Upwind Method: Finite Time

Time Steps:

The Upwind Method is:

\phi_i^{k+1}=\phi_i^k-\frac{c\Delta t}{\Delta x}(\phi_{i}^k-\phi_{i-1}^k)

Assume that the domain is from $$x=0$$ to $$x=3$$ and that the wave starts at $$t=0$$ and ends at $$t=T$$.

Choose the wave speed $$c$$, step size $$\Delta x$$, and the CFL number.

Note the calculated step time $$\Delta t$$ and the number of time steps which should be a multiple of 10, or no more than 10.

Click SOLVE to observe the initial condition in blue, the true solution in green, and the computed Upwind solution in red.

Initial Condition: $$e^{-200(x - .5)^2}$$

Wave Speed $$c=$$
$$\Delta x=$$
T =

The time step $$\Delta t$$ is:
The number of time steps is: