Magnetohydrodynamics (MHD) compressible turbulence¶

NOTE: This dataset is available in two different resolutions \(256^3\) for MHD_256 and \(64^3\) for MHD_64. The data was first generated at \(256^3\) and then downsampled to \(64^3\) after anti-aliasing with an ideal low-pass filter. The data is available in both resolutions.

One line description of the data: This is an MHD fluid flows in the compressible limit (subsonic, supersonic, sub-Alfvenic, super-Alfvenic).

Longer description of the data: An essential component of the solar wind, galaxy formation, and of interstellar medium (ISM) dynamics is magnetohydrodynamic (MHD) turbulence. This dataset consists of isothermal MHD simulations without self-gravity (such as found in the diffuse ISM) initially generated with resolution \(256^3\) and then downsampled to \(64^3\) after anti-aliasing with an ideal low-pass filter. This dataset is the downsampled version.

Associated paper: Paper

Domain expert: Blakesley Burkhart, CCA, Flatiron Institute & Rutgers University.

Code or software used to generate the data: Fortran + MPI.

Equation:

\[ \begin{align*} \frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{v}) &= 0 \\ \frac{\partial \rho \mathbf{v}}{\partial t} + \nabla \cdot (\rho \mathbf{v} \mathbf{v} - \mathbf{B} \mathbf{B}) + \nabla p &= 0 \\ \frac{\partial \mathbf{B}}{\partial t} - \nabla \times (\mathbf{v} \times \mathbf{B}) &= 0 \end{align*} \]

where \(\rho\) is the density, \(\mathbf{v}\) is the velocity, \(\mathbf{B}\) is the magnetic field, \(\mathbf{I}\) the identity matrix and \(p\) is the gas pressure.

Gif

Dataset	FNO	TFNO	Unet	CNextU-net
`MHD_64`	0.3605	3561	0.1798	\(\mathbf{0.1633}\)

Table: VRMSE metrics on test sets (lower is better). Best results are shown in bold. VRMSE is scaled such that predicting the mean value of the target field results in a score of 1.

About the data¶

Dimension of discretized data: 100 timesteps of 64 \(\times\) 64 \(\times\) 64 cubes.

Fields available in the data: Density (scalar field), velocity (vector field), magnetic field (vector field).

Number of trajectories: 10 Initial conditions x 10 combination of parameters = 100 trajectories.

Estimated size of the ensemble of all simulations: 71.6 GB.

Grid type: uniform grid, cartesian coordinates.

Initial conditions: uniform IC.

Boundary conditions: periodic boundary conditions.

Data are stored separated by (\(\Delta t\)): 0.01 (arbitrary units).

Total time range (\(t\_{min}\) to \(t\_{max}\)): \(t\_{min} = 0\), \(t\_{max} = 1\).

Spatial domain size (\(L_x\), \(L_y\), \(L_z\)): dimensionless so 64 pixels.

Set of coefficients or non-dimensional parameters evaluated: all combinations of \(\mathcal{M}_s=\){0.5, 0.7, 1.5, 2.0 7.0} and \(\mathcal{M}_A =\){0.7, 2.0}.

Approximate time and hardware used to generate the data: Downsampled from MHD_256 after applying ideal low-pass filter.

What is interesting and challenging about the data:¶

What phenomena of physical interest are catpured in the data: MHD fluid flows in the compressible limit (sub and super sonic, sub and super Alfvenic).

How to evaluate a new simulator operating in this space: Check metrics such as Power spectrum, two-points correlation function.

Please cite the associated paper if you use this data in your research:

@article{burkhart2020catalogue,
  title={The catalogue for astrophysical turbulence simulations (cats)},
  author={Burkhart, B and Appel, SM and Bialy, S and Cho, J and Christensen, AJ and Collins, D and Federrath, Christoph and Fielding, DB and Finkbeiner, D and Hill, AS and others},
  journal={The Astrophysical Journal},
  volume={905},
  number={1},
  pages={14},
  year={2020},
  publisher={IOP Publishing}
}