[FLASH-USERS] courant factor

Fri Apr 28 12:09:28 EDT 2017

Hi Riccardo :

  FLASH uses synchronous timestepping, so the the dt is the same across all
blocks. This simplifies the evolution algorithm considerably.

  Your simulation should be able to support a larger CFL number, even in 2D
axisymmetry. I just checked, and in Ji et al, 2013 (
http://adsabs.harvard.edu/abs/2013ApJ...773..136J), we used a CFL of 0.4 in
2D axisymmetry with unsplit MHD, though this was on a uniform mesh. The
fact that the crash is occurring early on does suggest an initialization
issue, or possibly a boundary issue in your run. I'd suggest outputting a
plotfile after the first timestep, and inspecting both it and the zeroeth
timestep plotfile very carefully. Is anything unusual occurring with the
velocity and/or sound speed? If so, where does the issue arise?

  Best wishes,

  Bob

On Fri, Apr 28, 2017 at 11:07 AM, Riccardo Ciolfi <
riccardo.ciolfi at oapd.inaf.it> wrote:

>
>  Dear Robert and Klaus,
>
> thank you very much for you reply.
>
> First, I would like to ask a clarification: does "global" delta_t mean
> that it is set the same in the entire block (but can still vary in
> different blocks) or it is the same in the entire computational domain of
> the simulation (i.e. in all the blocks)?
>
> To answer your question, my setup is purely hydro (an initial ball of
> matter in expansion, with a max expansion speed of 1e-4 c).
> In 1D it is a spherically simmetric expansion and cfl=0.8 is fine. In 2D I
> use axisymmetry and cylindrical coordinates with reflective bounday
> conditions on R_cyl=0 and outflow-type on R_cyl_max, z_min, and z_max.
> Could it be that the cfl is required very low close to the axis, thus
> compromising the choice of delta_t for the entire domain?
>
> The failure in 2D with any cfl larger than 0.1 is essentially at the
> beginning of the simulation.
>
> Thanks a lot!
>
>  Best,
>  Riccardo
>
>
>
> ----- Messaggio originale -----
> Da: "Robert Fisher" <rfisher1 at umassd.edu>
> A: "Klaus Weide" <klaus at flash.uchicago.edu>
> Cc: "Riccardo Ciolfi" <riccardo.ciolfi at oapd.inaf.it>,
> flash-users at flash.uchicago.edu
> Inviato: Venerdì, 28 aprile 2017 16:04:32
> Oggetto: Re: [FLASH-USERS] courant factor
>
> Dear Riccardo :
>
>   As Klaus indicates, a CFL number of 0.8 is generally sufficient, and 0.5
> is conservative. Requiring 0.1 may indicate some other issues in your
> initial condition and/or boundary conditions, which may be physical, but
> could also be a bug.
>
>   Can you also tell us when the crash is occurring? Shortly after
> initialization or well into the run?  This is an important clue as to what
> is happening.
>
>   It should be emphasized that the CFL condition is a necessary but not
> sufficient condition for numerical stability of a hydrodynamics code. This
> is because the condition itself is derived from a linearized analysis and
> can break down during strongly nonlinear evolution. For example, a strong
> acceleration or rapid cooling can drive the system unstable during a single
> timestep. For this reason, you will find problems with strong gradients in
> the initial condition, like shock tubes, often utilize a reduced initial
> timestep, and then "relax" to CFL. A reduced timestep can be set with the
> FLASH parameter dtinit.
>
>   Best wishes,
>
>   Bob
>
> On Thu, Apr 27, 2017 at 8:35 PM, Klaus Weide <klaus at flash.uchicago.edu>
> wrote:
>
> > On Thu, 27 Apr 2017, Riccardo Ciolfi wrote:
> >
> > > I am trying to understand the definition of the variable cfl. Does it
> > > correspond to the courant factor Delta_t/Delta_x * v_max?
> >
> > The timestep Delta_t is chosen such that
> >
> >    Delta_t/Delta_x * v_max  <=  cfl
> >
> > should be true in *each* cell (in 1D).
> >
> > > Is this the same at all levels, so that Delta_t is reduced by a factor
> > > of 2 together with Delta_x when moving to the next refinement level?
> >
> > There is only one global Delta_t.  Delta_x depends on the block.
> >
> > You can think of it as computing a local Delta_t for each cell, and the
> > global Delta_t is then the min of them.
> >
> > > Is there a simple way to enforce it?
> >
> > FLASH already does this for you.
> >
> > > I am using FLASH4.4 and for 1D hydro simulations I adopted the
> suggested
> > > clf=0.8 without any problem. When I move to 2D I cannot run unless I
> put
> > > cfl as low as 0.1. Is this expected?
> >
> > No, you should be able to uses larger values of cfl - as long as your
> > setup is purely a hydro problem.
> >
> > > For coordinates with
> > > Delta_x=Delta_y, shouldn't be sufficient to reduce the courant factor
> by
> > > a factor of sqrt(2)?
> >
> > See Hydro_computeDt for how exactly the computation is done for 2D and
> 3D.
> > But generally, a value of 0.8 or so should be good even for 2D.
> >
> > Are you using curvilinear coordinates?
> > Are you using additional physics that change the solution?
> > Do you have unusual or extreme initial or boundary conditions?
> >
> >
> > Klaus
> >
>
>
>
> --
> Dr. Robert Fisher
> Associate Professor / Graduate Program Director
> University of Massachusetts/Dartmouth
> Department of Physics
> 285 Old Westport Road
> North Dartmouth, Massachusetts 02747
> robert.fisher at umassd.edu
> http://www.novastella.org
>

-- 
Dr. Robert Fisher
Associate Professor / Graduate Program Director
University of Massachusetts/Dartmouth
Department of Physics
285 Old Westport Road
North Dartmouth, Massachusetts 02747
robert.fisher at umassd.edu
http://www.novastella.org
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