[FLASH-USERS] Question about numerical convergence of a radiative cooling layer

[Antoine Gintrand]

Dear Flash users,


I have a numerical problem and I was wondering if someone knows this kind
of issue.



In my astrophysical problem, I have a strong radiative cooling layer
separated by a

shock and a contact discontinuity.


In my simulation when the cooling is really strong, the gradients of
density, pressure and temperature become really strong too.

At some point there is in this layer two region, one is the cooling layer
and another is an extremely thin spike of cooled matter.


When I try a better refinement I find that the density spike of high
compression is 2 times greater if I multiply the refinement by 2

and actually, the density would diverge if I do not stop to increase the
refinement level at some point for the new simulations.

So I chose a refinement of the space to resolve the cooling layer very well
except for this spike of density near the contact discontinuity.


Then, I try to decrease the CFL condition coefficient to see if the
solution is sensitive to the decrease in time step.

The problem is that for each different simulations with different levels of
refinement,

the decrease in the CFL condition changes the numerical solution (and not
even in the same way for every different simulation with different spatial
refinement).

For example, in some simulations with a given refinement, I find the
formation of secondary shocks propagating

in the layer with high velocity when I decrease the CFL and in some others
I do not find them or I find really weaker ones.



I do not understand why because the time step dt calculated in the
simulation is

for every simulation at least 3 times of magnitude lower than the cooling
time step dt_cool during the simulation (I checked for all simulations).



The cooling time step in the simulation dt_cool is calculated as
dt_cool=0.5*pressure/(gamma-1)/Cooling   (Cooling in erg/s/cm^3 )

And dt << dt_cool for every simulation (see below)

                              t                   dt
                                                    dt_hydro   dt_cool
 CFL

 ******* 4.2186E+09 3.6423E-01  ( 1.151E+16, -1.000E+16,   0.00    ) |
 3.642E-01 1.073E+05 0.0400000
 ******* 4.2186E+09 3.6423E-01  ( 1.151E+16, -1.000E+16,   0.00    ) |
 3.642E-01 1.073E+05 0.0400000
 ******* 4.2186E+09 3.6423E-01  ( 1.151E+16, -1.000E+16,   0.00    ) |
 3.642E-01 1.073E+05 0.0400000
 ******* 4.2186E+09 3.6423E-01  ( 1.151E+16, -1.000E+16,   0.00    ) |
 3.642E-01 1.073E+05 0.0400000
 ******* 4.2186E+09 3.6423E-01  ( 1.151E+16, -1.000E+16,   0.00    ) |
 3.642E-01 1.073E+05 0.0400000
 ******* 4.2186E+09 3.6423E-01  ( 1.151E+16, -1.000E+16,   0.00    ) |
 3.642E-01 1.073E+05 0.0400000
 ******* 4.2186E+09 3.6423E-01  ( 1.151E+16, -1.000E+16,   0.00    ) |
 3.642E-01 1.073E+05 0.0400000
 ******* 4.2186E+09 3.6423E-01  ( 1.151E+16, -1.000E+16,   0.00    ) |
 3.642E-01 1.073E+05 0.0400000
 ******* 4.2186E+09 3.6423E-01  ( 1.151E+16, -1.000E+16,   0.00    ) |
 3.642E-01 1.073E+05 0.0400000



I would expect that the decrease in the CFL condition does not change so
much the solution in this case but actually changes

a lot the numerical solution after some times in the strong radiative
regime and my numerical solution seems to not be converged.



Thank you very much for any suggestions,



Best regards,



Antoine.
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