[Nek5000-users] Small diffusivity. How heat/diffusion equations are solved?

[nek5000-users at lists.mcs.anl.gov]

I am trying to model inner waves in a salinity-stratified solution,
for which kinematic viscosity is 10^-6, diffusivity is 10^-9, so Schmidt number is about 10^-3.
 If I set viscosity=diffusivity=10^-6, the program works fine, but I get too great effect of diffusion.
If I set diffusivity to be less than 10^-6, solution blows up.

In this connection I have two questions:

Is there a description how heat/diffusion equations are solved in nek5000?

Is it possible to change transport/diffusion equation just to transport equation, i.e. without diffusion at all?

Thanks.