AZEuS: An Adaptive Zone Eulerian Scheme

Introduction

AZEuS is a block-based adaptive mesh refinement (AMR) magnetohydrodynamics (MHD) astrophysical fluid code which employs ZEUS-3D as its underlying method (Clarke, 1996, 2010; ZEUS-3D website).

Virtually all AMR fluid codes to date are based on a zone-centred grid, with all hydrodynamical variables (density, energy, and momentum components) located at the centres of their respective zones. Magnetohydrodynamic solvers are designed with either zone-centred or face-centred magnetic field components, depending in part on the mechanism used to preserve the solenoidal condition. One such scheme is Constrained Transport (CT; Evans & Hawley, 1988), which places magnetic field components at the centres of the zone-faces to which they are normal. The staggered mesh introduced in such a scheme must be specifically accounted for in the AMR in such a way that the solenoidal condition remains zero everywhere -- including within the boundaries -- to machine round-off error (Balsara, 2001; Li & Li, 2004).

The only astrophysical fluid code in wide use that employs a fully-staggered grid, where the momentum components are also face-centred, are the ZEUS family of codes. To couple ZEUS with AMR and produce AZEuS, the block-based scheme of Berger & Colella (1989) has been modified for a fully-staggered grid, including the proper treatment of face-centred magnetic fields and face-centred momentum.

AZEuS is currently capable of solving problems in 1-D, 2-D, and 3-D in Cartesian, spherical polar, and cylindrical coordinates in both hydrodynamics (HD) and MHD. As with all ZEUS-type codes, additional physics modules are easily added. The EDITOR precompiler software is also used, which, among other things, provides for auto-parallelisation on shared-memory architectures (i.e., OpenMP).

Documentation

Methods paper: "AZEuS: An Adaptive Zone Eulerian Scheme for Computational MHD", Jon P. Ramsey, David A. Clarke, & Alexander B. Men'shchikov, 2012, ApJS, 199, 13.
User manual: Coming soon!

Downloads

Current version: v1.0 (2011-07-15)
The code will be made freely available for download (with registration) in the near future.

AMR Test Gallery

1-D tests:

1-D MHD shock tube test #2a of Ryu & Jones (1995): Animation

Four levels of refinement above a base grid of 40 zones are used, and successively darker shaded regions indicate higher levels of refinement. The dynamic refinement of grids is based on the detection of shocks, contact discontinuities, and gradients in v₂.

Variable legend: ρ = density

p = gas pressure
e_T = total energy
v_i = components of velocity (i = 1, 2, 3)
B_i = components of magnetic field (i = 2, 3)
Ψ = tan^-1 (B₃/B₂)

1-D MHD shock tube test #4a of Ryu & Jones (1995) using purely static mesh refinement: Animation

Plotted in the left column is the uniform grid solution with 1200 zones. In the middle column, the AMR solution with two static grids is shown. The right column shows the percent difference between the uniform grid and AMR solutions. Discounting zones inside discontinuities (which, even without AMR, are already in error by as much as 100% since discontinuities are supposed to be infinitely thin), the maximum error attributable to static grids in any of the variables is < 1%. One level of refinement above a base grid of 600 zones is used.

2-D tests:

MHD blast wave (Gardiner & Stone, 2005): Animation

Plotted are gas pressure (p; top left), density (ρ; top right), magnetic pressure (p_B; bottom left), and the distribution of AMR grids (bottom right) as a function of time using one level of refinement above a base grid of 200² zones.

Orszag-Tang MHD vortex (Orszag & Tang, 1979; Stone et al., 2008): Animation

Plotted are gas pressure (p; top left), specific kinetic energy (ρv²/2; top right), magnetic pressure (p_B; bottom left), and the distribution of AMR grids at level l = 3 (bottom right) as a function of time for a base grid of 128² zones. Twenty evenly spaced contours are shown between p = [0.03, 0.50], p_B = [0.0, 0.34], and ρv²/2 = [0.0, 0.19].

MHD accretion torus (Hawley, 2000; Mignone et al., 2007): Animation

Plotted are the logarithm of density (log ρ; top left), gas pressure (p; top right), poloidal field strength (|B| =sqrt [B_r² + B_θ²]; bottom left), and poloidal speed (|v| = sqrt[v_r² + v_θ²]; bottom right) as a function of time using one level of refinement above a base grid of (r , θ) = (296 x 128) zones. Boundaries of individual AMR grids are shown in white.

3-D tests:

Self-gravitational hydrodynamical collapse (Truelove et al., 1998): Animation (coming soon)

Additional tests will be added as they are performed.
For further details, please see the methods paper.
For test problems without AMR, visit the ZEUS-3D website.

Publications

"Simulating protostellar jets simultaneously at launching and observational scales", Jon P. Ramsey & David A. Clarke, 2011, ApJ, 728, L11 (Website)
"AZEuS: An Adaptive Zone Eulerian Scheme for Computational MHD", Jon P. Ramsey, David A. Clarke, Alexander B. Men'shchikov, 2012, ApJS, 199, 13.

Contact the developers

Current developers of AZEuS:	Jon P. Ramsey	ramsey (at) uni-heidelberg.de
	David A. Clarke	dclarke (at) ap.smu.ca
Past developers & contributors:	Alexander Men'shchikov

Acknowledgements

The development of AZEuS is supported, in part, by:

AZEuS

An Adaptive Zone Eulerian Scheme