Cactus Code Thorn VolumeIntegrals_GRMHDX
Author(s)    : Zachariah B. Etienne, Jay Kalinani
Note         : Thorn for integration of spacetime quantities, in
               integration volumes consisting of spherical shells,
               regions with hollowed balls, and simple spheres.

Usage example: Except for the definition of integrands, the
               behavior of this thorn is almost completely driven
               by the parameter file.

               Here's an example of a binary neutron star parameter
               file that performs a total of 6 integrals, computed
               every 32 timesteps. The neutron stars are originally
               centered at (+/-15.2,0,0) and have radii of a little
               less than 13.5 (equal-mass neutron stars):
               
               1. Integrate the entire volume with an integrand of 1.
                  (used for testing/validation purposes only).

               2. Perform all four integrals required to compute the
                  center of mass (numerator=3, denominator=1 integral):
                  COM^i = Integral(rho_star * x^i)/Integral(rho_star),
                  in an integration volume originally centered at
                  (x,y,z)=(-15.2,0,0) with a coordinate radius of 13.5
                  Also use the center of mass integral result to *SET*
                  the *ZEROTH* AMR center. In this way, the AMR grids
                  will track the center of mass as computed by this
                  integration.

               3. Same as (2), except use the integrand=1 (for validation
                  purposes, to ensure the integration volume is
                  approximately 4/3*pi*13.5^3). Also disable tracking of
                  this integration volume.

               4. Same as (2), except for the neutron star originally
                  centered at (x,y,z)=(+15.2,0,0).

               5. Same as (4), except use the integrand=1 (for validation
                  purposes, to ensure the integration volume is
                  approximately 4/3*pi*13.5^3). Also disable tracking of
                  this integration volume.

               6. Perform rest-mass integrals over entire volume.

VolumeIntegrals_GRMHD::NumIntegrals = 6
VolumeIntegrals_GRMHD::VolIntegral_out_every = 32
VolumeIntegrals_GRMHD::enable_file_output = 1
VolumeIntegrals_GRMHD::outVolIntegral_dir = "volume_integration"
VolumeIntegrals_GRMHD::verbose = 1
# The AMR centre will only track the first referenced integration quantities that track said centre.
#   Thus, centeroflapse output will not feed back into the AMR centre positions.
VolumeIntegrals_GRMHD::Integration_quantity_keyword[1] = "one"
VolumeIntegrals_GRMHD::Integration_quantity_keyword[2] = "centerofmass"
VolumeIntegrals_GRMHD::Integration_quantity_keyword[3] = "one"
VolumeIntegrals_GRMHD::Integration_quantity_keyword[4] = "centerofmass"
VolumeIntegrals_GRMHD::Integration_quantity_keyword[5] = "one"
VolumeIntegrals_GRMHD::Integration_quantity_keyword[6] = "restmass"

VolumeIntegrals_GRMHD::volintegral_sphere__center_x_initial         [2] = -15.2
VolumeIntegrals_GRMHD::volintegral_inside_sphere__radius            [2] =  13.5
VolumeIntegrals_GRMHD::amr_centre__tracks__volintegral_inside_sphere[2] =  0
VolumeIntegrals_GRMHD::volintegral_sphere__center_x_initial         [3] = -15.2
VolumeIntegrals_GRMHD::volintegral_inside_sphere__radius            [3] =  13.5

VolumeIntegrals_GRMHD::volintegral_sphere__center_x_initial         [4] =  15.2
VolumeIntegrals_GRMHD::volintegral_inside_sphere__radius            [4] =  13.5
VolumeIntegrals_GRMHD::amr_centre__tracks__volintegral_inside_sphere[4] =  1
VolumeIntegrals_GRMHD::volintegral_sphere__center_x_initial         [5] =  15.2
VolumeIntegrals_GRMHD::volintegral_inside_sphere__radius            [5] =  13.5

Maintainer(s): Jay Kalinani, Zachariah B. Etienne
License      : BSD 2-Clause (FreeBSD license)
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