# Center for Magnetic Self Organization

## in Laboratory and Astrophysical Plasmas

# Computational Tools

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**-The
NIMROD code solves the nonlinear equations of extended MHD as
an initial problem. Problems can be solved in either two or
three
dimensions. In three dimensions the geometry is restricted to
have at
least one periodic coordinate, but is otherwise arbitrary. (In
these
cases the dynamics remains fully three dimensional.) The extended
MHD
model includes both ideal and resistive MHD, and two-fluid (Hall
and
diamagnetic) and FLR (ion gyro-viscosity) corrections to Ohm's
law,
along with anisotropic thermal conductivity. The spatial
representation uses high (arbitrary) order finite elements for
the
non-periodic coordinates, and a dealised pseudo-spectral method
(with
FFTs) for the periodic coordinate. The time advance algorithm
is an
extension of that used in the DEBS code [D. D. Schnack, et al.,
J.
Comp. Phys. 70, 330 (1987)]. In particular, it uses a more accurate
semi-implicit operator, and introduces improved time centering
for the
two-fluid and gyro-viscous terms. Like DEBS, it 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). It has been applied to studies of several magnetic fusion
laboratory concepts, and to some astrophysical problems. The
basic
algorithm is described in C. R. Sovinec, A. H. Glasser, T.A.
Gianakon,
D. C. Barnes, R. A. Nebel, S. E. Kruger, D. D. Schnack, S. J.
Plimpton,
A. Tarditi, M. S. Chu, and the NIMROD Team, J. Comp. Phys. 195,
355
(2004). Further information about NIMROD can be found at

https://nimrodteam.org/index.html

**DEBS **-
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).

**Options
include:**

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.

established in coordination with the Department of Energy.