[Users] BSSN, 8th order accurate -- how much dissipation?

[Ian Hinder]

On 8 Apr 2019, at 18:03, Erik Schnetter <eschnetter at perimeterinstitute.ca<mailto:eschnetter at perimeterinstitute.ca>> wrote:

I am trying to set up a binary black hole simulation that uses 8th
order accurate finite differencing. (I need the black holes to be
highly resolved, and I don't need the wave zone, thus I am not use
AMR.) On the other hand, I am using Cartoon2D, and I extended it to
support 8th order interpolation.

My problem is that I cannot get the simulation started well. After a
few (about 70) time steps, the code aborts due to nans. Of course,
having modified thorn Cartoon2D, I cannot exclude that I made an error
there. On the other hand, I did find some pre-existing errors that I
corrected.

I wonder: What are good settings for numerical dissipation in this
case (ML_BSSN with fdOrder=8)? I see a sample parameter file that uses
epsDiss = 0.1; should I expect this to work? Would puncture initial
conditions need any kind of special treatment? (I'm using
TwoPunctures.)

Hi Erik,

I did experiments with this a while ago with a production BBH simulation (multipatch), and the limit seemed to be about 0.08 in my tests, and I use 0.05 for safety.  I don't have access to the data right now (though can dig it out if you want), but I think it was for a Courant factor of 0.45, though it might have been 0.5.  It is strongly dependent on the Courant factor.  You can probably get away with larger dissipation strengths for a short time or for low resolution, or if you don't have very sharp features (e.g. junk radiation from high spin or high q configurations), but you probably don't want to rely on this.

For reference, the parameters I use are below.

With Cartoon, I think you will have an effective very small grid spacing for small r, which means that to maintain the Courant condition, you would need a smaller timestep. Is that right?  I've never used Cartoon, but it seems like this is something that should be taken into account.

Puncture initial conditions shouldn't need any special treatment.  Without Cartoon, a resolution of something like 20 grid cells across the radius of the settled AH (which could be a factor of 2 larger than the initial radius) is probably a good minimum to use.


################################################################################
# Spatial finite differencing
################################################################################

SummationByParts::order                              = 8

# Drop order instead of using upwinded stencils, only for advection derivatives
SummationByParts::sbp_upwind_deriv = no

SummationByParts::sbp_1st_deriv                      = yes
SummationByParts::sbp_2nd_deriv                      = no
SummationByParts::onesided_interpatch_boundaries     = no
SummationByParts::onesided_outer_boundaries          = yes
SummationByParts::use_dissipation                    = no
GlobalDerivative::use_dissipation                    = yes
SummationByParts::scale_with_h                       = yes
SummationByParts::dissipation_type                   = "Kreiss-Oliger"

# Stability limit seems to be about 0.08
SummationByParts::epsdis                             = 0.05

# Variables for dissipation
SummationByParts::vars                               = "
  ML_BSSN::ML_log_confac
  ML_BSSN::ML_metric
  ML_BSSN::ML_trace_curv
  ML_BSSN::ML_curv
  ML_BSSN::ML_Gamma
  ML_BSSN::ML_lapse
  ML_BSSN::ML_shift
  ML_BSSN::ML_dtlapse
  ML_BSSN::ML_dtshift
"

--
Ian Hinder
Research Software Engineer
University of Manchester, UK

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