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.

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}
}