Consider an advection-diffusion problem
Now I want to remove the drift and rewrite the problem for the new domain. I use the change of variables $y=x-bt$, and the equation can be rewritten as
but what is the new domain in terms of variables $t$ and $y$?
Assume $b>0$, then $t\in [0,T]$ as before. But for $y$ the domain is not rectangular anymore, because it is like a triangle on one side. That is, for every fixed $t$, my $y$ is between $-bt$ and $\infty$? Did I compute the new domain correctly? If so, how do I solve this numerically? This is not a square box anymore, so do I have to place the grid for finite differences on such domain shape?