Shearing Box

Configuration

Nothing to do at the configuration for the shearing box.

Input File

The default shearing box setup requires the x1 (radial) direction to be shearing periodic, i.e. f (x, y, z) = f (x + L_x, y - qΩ₀ L _xt, z), where f (x, y, z) is a given variable, L_x is the x1 (radial) extent of the computational domain, q is the shearing rate, and Ω₀ is the local orbital frequency. It also requires the x2(azimuthal) direction to be exactly periodic with uniform grid spacing. In order to achieve that, one has to change the <mesh> block as follows:

    <mesh>
    ix1_bc     = shear_periodic   # inner-X1 boundary flag
    ox1_bc     = shear_periodic   # outer-X1 boundary flag
    ix2_bc     = periodic         # inner-X2 boundary flag
    ox2_bc     = periodic         # outer-X2 boundary flag
    x2rat      = 1.0              # X2 cell aspect ratio

The x3(vertical) boundaries may vary as the user's need. The other necessary shearing box parameters have to be specified are qshear, the shearing rate (1.5 for Keplerian rotation), and local orbital frequency Omega0, e.g.,

    <orbital_advection>
    Omega0     = 1.0             # orbital frequency
    qshear     = 1.5             # shearing rate
    shboxcoord = 1               # 1: default x-y shear; 2: 2D x-z case 

By default, the extra parameter shboxcoord is set to 1, i.e. shear in the x1-x2 (or horizontal x-y) plane; for 2D simulations in the vertical x-z plane, please set shboxcoord = 2, and ix1_bc/ox1_bc to shear_periodic boundaries (see pgen/hb3.cpp and input/mhd/athinput.hb3 for example).

Example 1:

The 2D hydro shearing sheet test:

    > python configure.py --prob=ssheet --flux=hlle --eos=isothermal

Example 2:

The 2D MRI test in x-z plane (shear velocity perpendicular to the plane):

    > python configure.py -b --prob=hb3 --flux=hlld --eos=isothermal

Example 3:

The 3D MRI/shwave test:

    > python configure.py -b --prob=hgb --flux=hlld --eos=isothermal 

Performance

Runs in the shearing box require additional computational cost compared to runs without the shearing box approximation. The cost comes from extra boundary calls and MPI communications of the sher periodic boundaries. We find only ~3% slow down, when running 3D MHD problems of 64³ grid points with MeshBlock size of 32³, with (hgb.cpp) and without (shock_tube.cpp) the shearing box boundary conditions. When compiling with the Intel compiler v18.0 and default optimization, and 8 processes are employed, the zone-cycles/second is 1.087 × 10⁷ for the former while 1.115 × 10⁷ for the latter.

Note

• Passive scalar is available even in the shearing box.
• AMR is prohibited and SMR is limited in the shearing box. When using SMR in the shearing box, all the meshblocks at the same z facing the x1 shear-periodic boundaries are required to have the same level.
• Orbital advection also works in the shearing box for shboxcoord = 1. See Orbital Advection.
• Both the PLM reconstructions (time/xorder=2 or time/xorder=2c) and the PPM reconstructions (time/xorder=3 or time/xorder=3c) are available in the shearing box. When giving time/xorder=4, however, the remapping in the shear periodic boundaries will be performed with only the 3rd-order spatial accuracy.
• Neither time/integrator=rk4 nor time/integrator=ssprk5_4 are allowed in the shearing box.