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Copyright 2016 Alexander (Sasha) Tchekhovskoy

HARMPI version 1.0 (released July 19, 2016)

A parallel, 3D version of HARM2D. The code is parallelized using MPI and is fully operational in 3D. Feel free to check out the user guide and exercises/homework.

Copyright 2006 Charles F. Gammie, Jonathan C. McKinney, Scott C. Noble, Gabor Toth, and Luca Del Zanna

HARM version 1.0 (released May 1, 2006)

This file is part of HARM. HARM is a program that solves hyperbolic partial differential equations in conservative form using high-resolution shock-capturing techniques. This version of HARM has been configured to solve the relativistic magnetohydrodynamic equations of motion on a stationary black hole spacetime in Kerr-Schild coordinates to evolve an accretion disk model.

You are morally obligated to cite the following two papers in his/her scientific literature that results from use of any part of HARM:

  1. Gammie, C. F., McKinney, J. C., & Toth, G. 2003, Astrophysical Journal, 589, 444 (paper, bibtex citation)
  2. Noble, S. C., Gammie, C. F., McKinney, J. C., & Del Zanna, L. 2006, Astrophysical Journal, 641, 626 (paper)

Further, we strongly encourage you to obtain the latest version of HARM directly from our distribution website.

HARM is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

HARM is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with HARM; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA


HARM is a conservative finite volume approach to solving the hyperbolic partial differential equations (PDE). Even though it was written with general relativistic magnetohydrodynamics (GRMHD) specifically in mind, it can solve almost any set of hyperbolic equations in conservation form:

dU / dt  +   dF(U) / dx^i   =  S(U)

where, if there is a set of equations, {U,F,S} are all state vectors and represent the set of conserved variables, fluxes and sources, respectively. There are also primitive variables, P, that are useful when solving hydrodynamic equations. Often, one only know how to calculate F given P, requiring the user to solve P(U) = U^{-1}(P). U(P) is a known algebraic set of equations in GRMHD, but P(U) is not so we are left to its calculation numerically. HARM performs most calculations with P and not with U, since one can derive all other MHD quantities from P efficiently (calculating P(U) is relatively slow compared to U(P)). Hence, the fluxes and sources are implemented here as functions of P.

The following are the files that comprise HARM. To the left are their names and on the right are short descriptions.

HARM includes the following files:

  • README : This file, contains general documentation
  • lic.txt : Text file of copyright information
  • COPYING : GNU Public License (GPL)
  • makefile : The makefile
  • main.c : Primary routine, calls major components of the code;
  • bounds.c : Boundary conditions (problem dependent);
  • coord.c : Specify/handle the user's coordinate system and metric;
  • decs.h : Header file incl. glob. arrays/vars., macros, compile-time parameters;
  • defs.h : Header file of definitions of those in decs.h
  • diag.c : Primary handler of all data output;
  • dump.c : Routine for writing grid functions at full precision over whole grid;
  • fixup.c : Routines for handling unphysical/unstable values of P and U ;
  • image.c : Routines for writing r8 or ppm raster images of grid functions;
  • image_interp.c : Supplemental program to interpolate an r8 file to x,y coordinates;
  • init.c : Procedures for calculating initial data;
  • interp.c : Slope-limiting/shock-capturing interpolation for Riemann solution;
  • lu.c : LU-decomp. and back-subst. routines for metric calculations
  • metric.c : Routines for doing tensor operations (inv., dot prod., lower/raising);
  • phys.c : For calculating U, F, S from P;
  • ranc.c : Random number generator;
  • restart.c : Checkpointing routines;
  • step_ch.c : Primary time-stepping routine and relatives;
  • u2p_defs.h : Inversion methods' main header file;
  • u2p_util.c : Misc. routines needed by inversion methods;
  • u2p_util.h : Header for u2p_util.h;
  • utoprim_1dfix1.c : P(U) assuming adiabatic or isothermal condition;
  • utoprim_1dvsq2fix1.c: Alternate version of utoprim_1dfix1.c
  • utoprim_2d.c : General GRMHD P(U) calculator with no assumptions;
  • map.ppm : PPM color map used to make images in PPM format;
  • maps : Directory containing other examples of color maps;
  • maps/blue-mono.ppm : Black-to-Blue map;
  • maps/bw.ppm : Greyscale (monochrome) map;
  • maps/color.ppm : 256-color map;
  • maps/green-mono.ppm : Black-to-Green map;
  • maps/red-mono.ppm : Black-to-Red map;

As in most finite volume programs, the numerical domain is discretized into parts called "cells." We assume that these cells are uniformly spaced with respect to code coordinates X1 and X2. One can, however, use a non-uniform set of coordinates (e.g. "r" and "theta") that are at least C-4 differentiable functions of X1,X2 (see bl_coord() in coord.c). Further, the user may specify any regular metric (arbitrary excision is not implemented) at compile-time in gcov_func() [coord.c].

HARM was written in a modular way so that methods can be easily interchanged. For instance, different slope limiters can be inserted into slope_lim() [interp.c], though HARM is currently hard-coded to have only two ghost zones per boundary. Currently only Lax-Friedrichs-type and HLL algorithms are implemented to calculate the numerical flux function, but other could be installed by altering fluxcalc() [step_ch.c]. A different set of PDE's can be solved by replacing primtoU(), primtoflux(), source(), vchar() [phys.c] and utoprim_2d() [utoprim_2d.c]. If the number of PDE's changed, though, one would have to change "NPR" [decs.h] and instances of arrays accessing indexes beyond current array allocations.

If you wish to use our algorithms and PDE's but want to change the initial conditions, then you need only change init.c and any compile-time parameters in decs.h (see below).


To get started, first make sure the settings in "makefile" are valid for your system. Once that is done, type the following commands:

prompt>  make
prompt>  ./harm 

to run the simulation. The current setting (128x64 cells) should be an acceptable size for any modern workstation. The code is configured to evolve the following initial conditions:

  • Kerr hole using Kerr-Schild metric, with a=0.9375 (BH normalized spin/M)
  • Fishbone-Moncrief torus w/ inner edge rin=6M, pressure max. at rmax=12M
  • Azimuthal vector potential component follows contours of constant density

The following files will be generated by HARM (using the default settings):

  • ./ener.out: accretion rates of rest-mass, total energy and angular momentum onto the black hole (plus other quantities, see diag.c for details)
  • ./dumps/dump[000-???] : double-precision, plain text output of grid functions (see dump.c for details)
  • ./images/im_*_[0000-????].ppm : dynamically-scaled snapshots of rho, bsq, u, the lorentz factor, and their logarithms at higher time resolution than the "dumps". Use ImageMagick's "display" command to view, and ppm2fli (see below) to animate.

Parameters that you may want to immediately adjust are:

  • decs.h: N1, N2 = number of cells in the X1 and X2 directions, respectively (X1 is the radial-going direction, X2 is the poloidal-going one).
  • init.c: a = spin of the black hole (spatial dimensions scale w/ black hole mass, i.e. M_BH = 1);
  • gam = adiabatic index for fluid;
  • rin = radial position of inner edge of torus;
  • rmax = radial position of pressure maximum;
  • beta = initial value of 2 P_max / b_max^2
  • Rout = radial coordinate of outer numerical boundary;
  • tf = end time of solution in units of black hole mass;
  • DTd = frequency of writing dump files in units of M
  • DTi = frequency of writing image files in units of M


The user has a choice of the types of images HARM makes: PPM or R8.
The former is a standard image format, see "man ppm" or the web for more details. R8 is an unmapped format of 1-bit in "color" depth, see image_r8() of image.c for details. R8 images are smaller in size since they do not provide the color scheme. Their downside is that after generating the R8 images, one must convert them to PPM or some other format with a user-supplied parsing program. We have left this R8 conversion utility as an exercise for the user, but have provided the PPM format for those of you who are lazy and want to see pictures immediately.

  • ppm: animate ppm files with either convert im_lrho*.ppm im_lrho.gif or use ppm2fli
  • r8: raw format that can be easily converted to a ppm file.

The format of the dump files can be easily gleaned from dump() in dump.c.


Please send any bug reports to


  • HARM version 1.0 released to the general public under the GPL on May 1st, 2006
  • HARMPI v1.0 released on July 19 2016


3D massively parallel general relativictic MHD code HARMPI







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