Methods for 1D Advection

Copyright (C) 2010-2020 Luke Olson
Copyright (C) 2020 Andreas Kloeckner

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Problem Description

We will set up the problem for $$ u_t + u u_x = 0$$ with periodic BC on the interval $[0,1]$.

Set up the Grid

Now define an initial condition:

Setting the Time Step

Have spatial grid. Now we need a time step. So define a ratio parameter $\lambda$. Let $$ \Delta t = \Delta x \frac{\lambda}{c}$$

Now make an index list, called $J$, so that we can access $J+1$ and $J-1$ easily

Run and Animate

Experiments: