[Users] Implementing a simple 1+1 BSSN in Python

Chris Stevens chris.stevens at canterbury.ac.nz
Fri May 13 20:58:48 CDT 2022

Hi all,

I've been having trouble implementing the BSSN equations, as given by CTGamma, in Python using the package COFFEE, which I am very familiar with:


The main comments are:

-- For simplicity, I am starting with a 1+1 code (set 2/3 spatial derivatives to be exactly zero).
-- The 1+log slicing for the lapse and a zero shift.
-- The "phi" conformal factor type
-- The evolution equations are written to Python by a very slight modification of the .m file in CTGEvolution. I've confirmed this .m file outputs the same file that is in the src directory.
-- The vanishing of the trace of A is enforced after each full timestep in the same way as CTGamma.
-- Boundary conditions are not applied.
-- Fourth order SBP operators that lean over toward the boundaries are used.
-- Minkowski initial data with all fields zero except \gamma11/22/33.
-- Euler step is used for time integration to easier compare between Python and the Einstein toolkit.

This leads to a stable evolution in the Einstein toolkit with the attached .par file using a simple one patch Cartesian grid. However, in Python, I get that fields diverge, starting at the boundaries and then propagating inward (including with RK4). This behaviour does not go away with higher resolution or reduced CFL. It is however, fixed completely by setting the second spatial derivative of \alpha to be exactly zero. Trying many different SBP FD operators that have proved successful for other projects has not changed the behaviour.

The COFFEE code has been used and tested in a variety of projects and so there should not be a problem here. Thus, the only thing I can think of, is that the Einstein toolkit is doing something that I am not realizing, that is helping it remain stable. Hopefully, somebody on this mailing list might have an idea?

Thanks in advance,




Dr Chris Stevens

Lecturer in Applied Mathematics

Rm 602, Jack Erskine building

School of Mathematics and Statistics

T: +64 3 369 0396 (Internal 90396)

University of Canterbury | Te Whare Wānanga o Waitaha

Private Bag 4800, Christchurch 8140, New Zealand



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