[aspect-devel] steady state problem

[Wolfgang Bangerth]

> we are currently looking at benchmark-type problems and we are only 
> interested in the steady state of the system.
> Long story short, we would like for instance to run the Blankenbach 
> experiment (i.e. convection-box.prm) and arrive at steady state
> as fast as possible since we are not interested in the time evolution of 
> the model: ideally we would like to arrive after 1 timestep at the
> steady state solution,

That's going to be difficult because the problem is nonlinear and you 
somehow have to iterate out this nonlinearity. Time stepping is one 
method to achieve this. Did you take a look at the cookbook in the 
manual that shows how to set up an example where I'm only interested in 
the steady state?

> or in other words we would like to zero the \rho 
> c_p dT/dt term in the heat transport equation.
> We have (naively) tried this approach by zeroing the term bdf2_factor * 
> scratch.phi_field[i] * scratch.phi_field[j])in advection.cc 
> <https://urldefense.proofpoint.com/v2/url?u=http-3A__advection.cc&d=DwMFAg&c=ODFT-G5SujMiGrKuoJJjVg&r=KkOrCga5IcWjxrpeTIn1nmQG6jJSnwzdZwfNniMeeCc&m=ogr2JJ9z8kM0HK_cqi8xzJSLCogoCEPeGwe6Af_wgpA&s=WRmWoLRpZXp7UtehYlrBbUbRabw1sZ0P-ltbulQAK0I&e=> .
> 
> Unsurprisingly, this did not work and the code aborted. Instead of 
> zeroing the term, we tried placing in front of it a coefficient alpha=0.5

This only re-scales the time variable. This does not actually make the 
problem simpler -- it it equivalent to just taking a larger time step 
(which you can achieve by selecting a larger CFL number).


> but this lead to a temperature field which on average was twice as large 
> as the initial one. (if alpha=0.25, then it is approx 4times larger).
> We suspect that this alpha coefficient of ours probably should come in 
> somewhere else too

Yes. There is a corresponding term on the right hand side because where 
you put it is one half of the term
   (T_n - T_{n-1} ) / dt


Best
  W.

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