NIMROD|| FLASH || DEBS

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
http://nimrod.txcorp.com:8080/nimrodbeta

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.