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

[Wolfgang Bangerth]

> Suggestions:
> 1. Density should always be positive and we should enforce this in
> debug mode with an Assert. What to do in release mode? Should we
> restrict the density to something sensible?
> 2. The material model 'simple' should simply clamp the compositional
> fields to [0,1].
> 3. If the user specifies that a compositional field is supposed to be
> in [0,1], should we postprocess the field and restrict it to [0,1]? I
> think not, because we would lose mass this way (we could restrict it
> only for output and material models but use the original one in the
> next timestep).

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.

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?

Best
  W.

-- 
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Wolfgang Bangerth               email:            bangerth at math.tamu.edu
                                 www: http://www.math.tamu.edu/~bangerth/