Hi.  I am interested in getting guidance on how finely to discretize
the domain when solving 1-D a) Burgers (advection/diffusion) equation and
b) the same equation with a reaction term:

dC/dt = -u* dC/dx + D* d2C/dx2
dC/dt = -u* dC/dx + D* d2C/dx2 - kC
dC/dt = -u* dC/dx + D* d2C/dx2 - k*(C-C') where C' is a constant

The problem is reacting flow, say, water adsorption on a silica gel, or the like.

I recall numerical dispersion is proportional to dx (or dx**2) in the first
equation; please confirm and expand.  How does the accuracy of my
solution (amplitude and phase) relate to my choice of dx? Can you
provide guidance for the 2nd/3rd equation?

Where do you get u? I guess since it's a 1-D problem, u is a constant?
In that case, you can drop the advection term by switching to a frame
of reference moving with the flow, so a) reduces to the heat equation.

I don't think any of your equations is technically Burger's equation,
which has a nonlinear term of the form C* dC/dx.