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Manuscript Title: R-MHD: an adaptive-grid radiation-magnetohydrodynamics computer code.
Authors: O. Yasar, G.A. Moses
Program title: R-MHD
Catalogue identifier: ACGN_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 69(1992)439
Programming language: Fortran.
Computer: CRAY X-MP.
Operating system: UNIX, UNICOS.
Word size: 64
Peripherals: disc, graph plotter.
Keywords: Plasma physics, Mhd, Adaptive grid, Equidistribution Principle, Nuclear fusion, Plasmas, Confinement inertial Fusion, Hydrodynamics radiation, Magnetohydrodynamics.
Classification: 19.10.

Subprograms used:
Cat Id Title Reference
ABJT_v1_0 IONMIX CPC 56(1989)259

Nature of problem:
Radiation processes and radiation transport play an important role in inertial confinement fusion (ICF) plasmas. The dynamics of target implosion, and of the plasma channels can be strongly affected by radiative transfer. The coupling between the plasma, radiation and magnetic fields in light ion beam transport channels must be accurately determined to predict and interpret the outcome of ICF experiments.

Solution method:
The problem involves continuity, momentum and energy equations for the plasma, and field intensity equations for radiation and magnetic fields. These governing equations are solved on an adaptive grid system where mesh points follow dynamically the steep gradients to provide better resolution. The adaptive mesh generation is based on the equidistribut- ion principle and an explicit procedure is followed to update the mesh distribution in time. The plasma equations are also solved explicitly using donor-cell spatial differencing. The timestep control is done through CFL condition and a constraint on the time-rate change of plasma energy. Since the timestep is chosen to be on the order of plasma timescale, the radiation and magnetic field equations are solved implicitly considering the fact that they would have required a smaller timestep if they were solved explicitly. The radiation transfer equation describes how photons travel in the medium, thus it requires angular dependent solution of the specific intensity. The multigroup radiative transfer equation is solved for discrete angles and energy groups which makes the solution a detailed one but a necessary one because any approximation (e.g., diffusion) to have a shortcut solution might have sacrificed the accuracy of the results. The discrete ordinate SN method with any number of discrete angles would be very close to the real answer. Since the equation is also discretized for the photon energy groups, there is a need for groupwise opacity data which is found from an atomic physics code published earlier in this journal. The equation of state data for plasma equations is also obtained from this code.

Restrictions:
Our radiation-magnetohydrodynamics (R-MHD) code is one-dimensional, assuming symmetry in all other directions. The plasma is considered in the magnetohydrodynamics (MHD) frame, thus it is assumed non- relativistic and it involves low frequencies. Although the code was originally designed for inertial confinement fusion plasmas, it can be applied to any compressible flow. When applied to plasmas, it should be noted that ions and electrons are assumed to have the same temperature. Regarding the numerics, the physical problem is solved on an adaptive grid system that is generated through an explicit procedure. The resolution via mesh refinement could be as low as 10**-2 - 10**-4 factor of the initial uniform mesh spacing. The discrete ordinate method used to solve the radiation field intensity is based on S6, although one can try to modify this for a higher number of angles.

Unusual features:
R-MHD code involves a great deal of physics including the mesh adaptivity scheme, fluid dynamics, particle transport and radiation- magnetohydrodynamics. It is written in FORTRAN 77 and best handled in a UNIX environment with make utilities.

Running time:
The CPU time largely depends on the simulation time and the number of photon energy groups. For a run with 20 energy groups and a simulation time of 2 mu seconds, the code takes 3 - 5 minutes on CRAY Y-MP. This time may go up to 30 - 40 minutes for 200 energy groups. The hydrodynamic part does not seem to be a problem timewise, but the detailed solution of radiation field is, when used with a large number of groups.