Center for Magnetic Self Organization
in Laboratory and Astrophysical Plasmas
FLASH-is a modular, adaptive-mesh,
parallel simulation code capable of
handling general flow problems found in many physical, astrophysical
and laboratory environments. In order to achieve this goal the code provides a set of algorithmic modules to compute equations of classic and relativistic hydrodynamics and magnetohydrodynamics that are coupled with general equations of state, material property models, various networks of atomic and nuclear reactions and self-gravity. The code is designed to allow users to configure problems, change algorithms and add new physics modules with minimal effort. It uses the PARAMESH library to manage a block-structured adaptive grid and the MPI library to achieve portability and scalability on a variety of different parallel computers.
NIMROD code solves the nonlinear equations of extended MHD as
an initial problem. Problems can be solved in either two or
dimensions. In three dimensions the geometry is restricted to
least one periodic coordinate, but is otherwise arbitrary. (In
cases the dynamics remains fully three dimensional.) The extended
model includes both ideal and resistive MHD, and two-fluid (Hall
diamagnetic) and FLR (ion gyro-viscosity) corrections to Ohm's
along with anisotropic thermal conductivity. The spatial
representation uses high (arbitrary) order finite elements for
non-periodic coordinates, and a dealised pseudo-spectral method
FFTs) for the periodic coordinate. The time advance algorithm
extension of that used in the DEBS code [D. D. Schnack, et al.,
Comp. Phys. 70, 330 (1987)]. In particular, it uses a more accurate
semi-implicit operator, and introduces improved time centering
two-fluid and gyro-viscous terms. Like DEBS, it is efficient
accurate for problems related to deviations from equilibrium
spatially and temporally stiff systems; it is not designed for
that are dominated by advection (e.g., strong turbulence and
waves). It has been applied to studies of several magnetic fusion
laboratory concepts, and to some astrophysical problems. The
algorithm is described in C. R. Sovinec, A. H. Glasser, T.A.
D. C. Barnes, R. A. Nebel, S. E. Kruger, D. D. Schnack, S. J.
A. Tarditi, M. S. Chu, and the NIMROD Team, J. Comp. Phys. 195,
(2004). Further information about NIMROD can be found at
The DEBS code solves the three-dimensional, compressible, non-linear,
resistive MHD equations as an initial value problem in doubly
periodic cylindrical geometry. It uses a staggered finite-difference
grid in the radial coordinate, and de-aliased pseudo-spectral
representations (with FFTs) for the periodic theta and z coordinates.
The time advance incorporates a centered leapfrog method for
wave-like terms, and a predictor-corrector method (with upwind
radial differencing) for the advective terms. A semi-implicit
algorithm provides unconditional numerical stability with respect
to waves. The time step is only limited by advective stability
and accuracy. The algorithm is efficient and accurate for problems
related to deviations from equilibrium in spatially and temporally
stiff systems; it is not designed for problems that are dominated
by advection (e.g., strong turbulence and shock waves).
a) ideal MHD;
b) fully three-dimensional temperature dependent resistivity;
b) simple viscosity;
c) anisotropic thermal conductivity;
d) independently rotating inner and outer boundaries (for studying rotational stability, for example);
e) mean flows;
f) imposed external fields (e.g., field errors);
g) multiple non-ideal (resistive) outer boundaries;
h) linear stability;
i) hydrodynamics (no magnetic field).
DEBS has been extensively used and benchmarked for over a decade by laboratory plasma research groups. The algorithm is documented in D. D. Schnack, Z. Mikic, D. S. Harned, E. J. Caramana, and D. C. Barnes, J. Comp. Phys. 70, 330 (1987). Significant applications of DEBS are described in the book S. Ortolani and D. D. Schnack, "Magnetohydrodynamics of Plasma Relaxation", World Scientific Press, Singapore, 1993.