AZEuS: Adaptive Zone Eulerian Scheme

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


All astrophysical AMR fluid codes in use today are based on a zone-centred method, with all hydrodynamical variables (density, energy, and momentum components) located at the centres of their respective zones. AMR MHD 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 locates 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 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 (e.g., Balsara, 2001; Li & Li, 2004).

One of the few astrophysical fluid codes in wide use that employ a fully-staggered grid, where the momentum components are face-centred like the magnetic fields, are the ZEUS family of codes. In order to couple ZEUS with AMR and produce AZEuS, the block-based scheme of Berger & Colella (1989) was modified for the fully-staggered mesh, 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 single grid and AMR modes. Physical regimes currently available are: hydrodynamics (HD), ideal MHD, and radiation hydrodynamics (RHD; with flux-limited diffusion [FLD] and a simple ray-tracer). As with all ZEUS-type codes, additional physics modules are easily added. The EDITOR pre-compiler software is also (still) used, which, among other things, provides for auto-parallelisation on shared-memory architectures (i.e., OpenMP).



The new version of the AZEuS website has been launched.


  1. “Radiation hydrodynamics including irradiation and AMR with AZEuS”, J.P. Ramsey, C.P. Dullemond, 2014, submitted to A&A (astro-ph/1409.3011).
  2. “AZEuS: An Adaptive Zone Eulerian Scheme for Computational MHD”, J.P. Ramsey, D.A. Clarke, A.B. Men’shchikov, 2012, ApJS, 199, 13.
  3. “Simulating Protostellar Jets Simultaneously at Launching and Observational Scales”, J.P. Ramsey, D.A. Clarke, 2011, ApJ, 728, L11 (Paper website).


A user’s manual is under development; it will be placed here when finished.


If you are interested in working with AZEuS, please contact either Jon Ramsey or David Clarke .


Current developers & contributors: Affiliation Contact
Jon P. Ramsey Institut für Theoretische Astrophysik, Universität Heidelberg, Germany ramsey (at)
David A. Clarke Institute for Computational Astrophysics, Saint Mary’s University, Halifax, Nova Scotia, Canada dclarke (at)
Chris MacMackin    
Past developers & contributors:  
Alexander Men’shchikov  
Samantha Pillsworth  


The continued development of AZEuS is made possible, in part, by the following organisations:

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