[aspect-devel] cookbooks/composition-active.prm

[Timo Heister]

> Is it really a problem with the compositional field? I think you could
> reproduce this if you had no compositional field but instead used a
> temperature dependent density of the form
>
>   rho(T) = - alpha T
>
> as is often done when non-dimensionalizing the problem and subtracting the
> static pressure. Here, if your temperature becomes negative (completely
> reasonable if T is non-dimensionalized), then rho becomes negative.

Okay. You are right that computations with negative density
(variations) could be okay. My assumption is that by doing
max(density) over a cell we get an inconsistent sign of  \nabla \cdot
(k+nu) \nabla T. Here nu is multiplied with a positive max_density
instead of the locally negative density.

Also, it looks like composition-active.prm does work with linear
temperature elements (even though the density still becomes negative).

> To me, what it boils down is that in the cases you describe, the density is
> not physical. Rather, it is the *deviation* from a physical density, which
> is fine in the equations if you just describe the pressure as the deviation
> from the hydrostatic pressure. In cases like this, of course, multiplying
> with the deviation from a physical density makes no sense -- in fact, it may
> be that the whole temperature equation makes no sense since it reads
>
>   rho * c_p * DT/Dt + ...
>
> instead of
>
>   (rho_0 + drho) * c_p * DT/Dt + ...
>
> Or do I misunderstand something?

It certainly makes a difference to add a rho_0 to this equation. So,
do we need to differentiate between the cases where rho is a variation
or not?

-- 
Timo Heister
https://urldefense.proofpoint.com/v1/url?u=http://www.math.clemson.edu/~heister/&k=dsHy%2FVymniCD0osh6tze%2Fw%3D%3D%0A&r=WLGUy1n%2F1Vzsqown7KFPcAEzR5DIdbP771jYw4Spy%2Bk%3D%0A&m=JuM0yt%2F6jWUFcQZyFdtJdX0E6Fx5uUJ89gMhJvP0%2Fws%3D%0A&s=e58da1ae982842cf314cd656584321e6b931343f771d105c95534de91729bca9