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3D Circularly Polarized Alfven Wave

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evazlimen edited this page Sep 23, 2023 · 1 revision

3D Circularly Polarized Alfven Wave

This is an exact nonlinear solution to the MHD equations. It is often used for convergence testing and to test how the code handles nonlinearity. Parameters from Gardiner & Stone 2008. The test consists a density of 1.0 and pressure of 0.1 with a right polarized moving wave of amplitude 0.1 and wavelength 1.0. The magnetic field is initialized as 1 $\hat{x}$. This test is performed with the mhd build (cholla/builds/make.type.mhd). Full initial conditions can be found in cholla/src/grid/initial_conditions.cppunder Circularly_Polarized_Alfven_Wave().

Parameter file: (cholla/examples/3D/cicularly_polarized_alfven_wave.txt)

#
# Parameter File for the circularly polarized Alfven Wave
# See [Gardiner & Stone 2008](https://arxiv.org/abs/0712.2634) pages 4134-4135
# for details.
#

################################################
# number of grid cells in the x dimension
nx=64
# number of grid cells in the y dimension
ny=32
# number of grid cells in the z dimension
nz=32
# final output time
tout=1.0
# time interval for output
outstep=1.0
# name of initial conditions
init=Circularly_Polarized_Alfven_Wave
# domain properties
xmin=0.0
ymin=0.0
zmin=0.0
xlen=3.0
ylen=1.5
zlen=1.5
# type of boundary conditions
xl_bcnd=1
xu_bcnd=1
yl_bcnd=1
yu_bcnd=1
zl_bcnd=1
zu_bcnd=1
# path to output directory
outdir=./

#################################################
# Parameters for linear wave problems
# Polarization. 1 = right polarized, -1 = left polarized
polarization=1.0
# velocity in the x direction. 0 for moving wave, -1 for standing wave
vx=0.0
# pitch angle
pitch=0.72972765622696634
# yaw angle
yaw=1.1071487177940904
# value of gamma
gamma=1.666666666666667

Upon completion, you should obtain 2 output files. The initial and final densities and total pressures (in code units) of a slice along the y-midplane is shown below. Examples of how to plot projections and slices can be found in cholla/python_scripts/Projection_Slice_Tutorial.ipynb.
Two 2D histograms side by side, showing density of cells in the z direction vs cells in x direction. The leftmost is the initial density plot with a constant density of 1 throughout all cells. The rightmost plot is the final density plot at t = 1.00 with a nonconstant density in x and z. The density distributed is striped, a repeating pattern ofvalues of 0.999, 1.000, 1.001, 1.000. These stripes are at a 45 degree angle to the x and z axes, slanting downwards.
Two 2D histograms side by side, showing pressure of cells in the z direction vs cells in x direction. The leftmost is the initial pressure plot with four slanted bands, each at a 45 degree angle to the x and z axes of alternating pressure. Beginning at the lower left corner, they alternate between 0.4368 and 0.4366, with the lower density bands being slightly wider. The rightmost plot is the final pressure plot at t = 1.0. Again there is a repeating pattern of slanted bands but a greater variation in pressure is seen. A band of 0.4365 transitions to 0.4366 to 0.4367 to 0.4368 briefly, then the bands decrease to 0.4365 and restart the cycle.

By changing the outstep to 0.01, you will obtain 101 output files and can obtain the evolution of the magnetic field in the z direction (here at 10 fps):

circularly-polarized-alfven-wave-bz.mp4

We see the wavefronts advancing towards the upper right, notably remaining planar.

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