[FLASH-USERS] issues with radiative cooling shocks

[Antoine Gintrand]

Dear flash users,

I have an issue that has been troubling me for a long time.
I do the simulation of a strong shock in the interstellar medium that cools
with a source term according to the cooling tables of *Sutherland* &
*Dopita* (1993).

the problem comes when the cooling becomes strong and I receive the
following message :

       n          t                      dt                 (         x,
       y,          z) |                    dt_hydro  dt_Cool   CFL

 253369 8.7315E+09 2.1942E+03  ( 1.773E+16, -8.164E+15,   0.00    ) |
 2.194E+03 4.696E+04 0.1000000
  253370 8.7315E+09 2.1958E+03  ( 1.773E+16, -8.164E+15,   0.00    ) |
 2.196E+03 4.687E+04 0.1000000
  253371 8.7315E+09 3.0850E+01  ( 1.864E+16, -7.383E+15,   0.00    ) |
 3.085E+01 4.678E+04 0.1000000
  253372 8.7315E+09 2.4375E-01  ( 1.864E+16, -7.383E+15,   0.00    ) |
 2.438E-01 4.678E+04 0.1000000
  253373 8.7315E+09 2.4375E-01  ( 1.864E+16, -7.383E+15,   0.00    ) |
 2.438E-01 4.678E+04 0.1000000
  253374 8.7315E+09 2.4375E-01  ( 1.864E+16, -7.383E+15,   0.00    ) |
 2.438E-01 4.678E+04 0.1000000
  253375 8.7315E+09 1.0000E-10  ( 1.864E+16, -7.383E+15,   0.00    ) |
 1.745E-16 2.569E+02 0.1000000
  253376 8.7315E+09 1.0000E-10  ( 1.864E+16, -7.383E+15,   0.00    ) |
 1.289E-60 2.569E+02 0.1000000
 dtCheck=   0.0000000000000000
 DRIVER_ABORT: [Hydro]: Computed dt is not positive! Aborting!

and I can see that the pressure drops dramatically so the movement of
matter accelerates and the compression increases drastically.
I believe that this is maybe due to the catastrophic instability of Falle
(1981).
Indeed, the cooling time becomes smaller than the time needed for the sound
wave to travel the cooling region
and the pressure could not be stable anymore so it begins to fall inside
this region.
The problem is that during the process, the region becomes poorly resolved
and the gradient of pressure density and temperature are very high.
Also, the problem is that when I increase the resolution, the code fails at
earlier times because the cooling and the compression are even more
efficient.
When I chose a lower cfl coefficient it would just delay the fail message.

One idea that seems to work would be to use some artificial viscosity but I
do not know if this would be consistent and the physical meaning of this.
Indeed when I increase the coefficient of artificial viscosity (cvisc),  at
some value of the parameter (cvisc=1.5), the simulation will continue to
run but the time step drops a lot.

Is anyone have some ideas to solve this issue,

Thank you for your help,

Best regards,

Antoine Gintrand.
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