Viscosity terms break Rayleigh-Taylor symmetry

[felker]

Bug report

Summary of issue

Reporting on behalf of Ben Ryan @ LANL.

The diffusion processes module added in #123 do not maintain mirror symmetry when solving the Rayleigh-Taylor problem.

Steps to reproduce
./configure.py --prob=rt -hdf5 -mpi --nghost=3

Input file:
athinput.rt2d_visc_nompi.txt

Expected outcome
Exact symmetry still preserved using PPM, multiple MeshBlocks on a uniform Cartesian grid in the zero viscosity case.

Actual outcome
When using problem/nu_iso= 0.000001 with PPM, a visible asymmetry results, regardless if using MPI or not:

No visible asymmetry is seen when using PLM with the above input file. No nonzero values are observed in the HDF5 output when calculating the differences to single precision in Python. However, from my tests in #98, I would expect such differences to occur with PLM at values smaller than 32-bit machine precision.

Version info

• Athena++ version: e144ec6
• Compiler and version: gcc 7.3.0
• External library versions (if applicable): With and without OpenMPI 2.1.0

[felker]

An update: I have confirmed that the asymmetry also occurs with PLM when viscosity is enabled. It is much smaller than when using PPM, but you can see in the attached plots of the final density and symmetry errors that the differences are nonzero. The differences appear immediately in the first output. The final maximum density asymmetry is 3.44452022460473e-10, which you wouldn’t be able to observe when viewing the results at single precision in Python.

I generated these results from athinput.rt2d_visc_mpi with time/xorder=2. The asymmetry disappears if problem/nu_iso=0.0. The same behavior is seen with PPM.

I will try to replicate the symmetry fix for AMR/SMR I made in ced843d for viscosity.cpp stencils.

rt-plm-visc-nx1-288-mbnx1-24.pdf

[felker]

Fixed in e8e4f64. May not have found all sources of asymmetry, but I changed the associativity of 3x stencils in viscosity.cpp and added signed comments indicating their fragility.

Correct PPM solution for athinput.rt2d_visc_mpi is attached.

rt-ppm-visc-fixed-nx1-288-mbnx1-24.pdf