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3D Ryu Jones 1a

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evazlimen edited this page Sep 23, 2023 · 1 revision

3D Ryu and Jones MHD shock tube 1a

This MHD shock tube has five waves and does not induce alfven waves. Parameters from Ryu & Jones 1995. For more testing information see MHD Riemann Problems. The test consists of a left state with density of 1.0, pressure of 20.0 and velocity of 10.0 $\hat{x}$. The right state consists of a density and pressure of 1.0 and velocity of -10.0 $\hat{x}$. Both sides have a magnetic field of 1.4104739588693909 $\hat{x}$ + 1.4104739588693909 $\hat{y}$. Gamma is set to 1.6666666666666667 and the initial discontinuity is at 0.5. This test is performed with the mhd build (cholla/builds/make.type.mhd).

Parameter file: (cholla/examples/3D/Ryu_and_Jones_1a.txt)

While the file states that it is for test 4d, it is for test 1a.

#
# Parameter File for 3D Ryu & Jones MHD shock tube 4d.
# Citation: Ryu & Jones 1995 "Numerical Magnetohydrodynamics in Astrophysics:
# Algorithms and Tests for One-Dimensional Flow"
#
# Note: There are many shock tubes in this paper. This settings file is
# specifically for shock tube 4d
#

################################################
# number of grid cells in the x dimension
nx=256
# number of grid cells in the y dimension
ny=256
# number of grid cells in the z dimension
nz=256
# final output time
tout=0.08
# time interval for output
outstep=0.08
# name of initial conditions
init=Riemann

# domain properties
xmin=0.0
ymin=0.0
zmin=0.0
xlen=1.0
ylen=1.0
zlen=1.0

# type of boundary conditions
xl_bcnd=3
xu_bcnd=3
yl_bcnd=3
yu_bcnd=3
zl_bcnd=3
zu_bcnd=3

# path to output directory
outdir=./

#################################################
# Parameters for 1D Riemann problems
# density of left state
rho_l=1.0
# velocity of left state
vx_l=10.0
vy_l=0.0
vz_l=0.0
# pressure of left state
P_l=20.0
# Magnetic field of the left state
Bx_l=1.4104739588693909
By_l=1.4104739588693909
Bz_l=0.0

# density of right state
rho_r=1.0
# velocity of right state
vx_r=-10.0
vy_r=0.0
vz_r=0.0
# pressure of right state
P_r=1.0
# Magnetic field of the right state
Bx_r=1.4104739588693909
By_r=1.4104739588693909
Bz_r=0.0

# location of initial discontinuity
diaph=0.5
# value of gamma
gamma=1.6666666666666667

Upon completion, you should obtain two output files. The initial and final densities (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 value of 1.0 across all cells. The rightmost plot is the final density plot at t = 0.08 with a constant density in z and nonconstant in x. From left to right, a density of 1 jumps to a value of 2.5 at x = 40 cells, followed by a jump to 3.9 at x = 150 cells and a drop to 3.85 at c = 160 cells. There is a final density drop to 1.0 at x = 225 cells.

A skewer in x along y and z midplanes yields the 1-dimensional solution. $\psi$ is defined at $\tan^{-1}\left(\frac{B_{z}}{B_{y}}\right)$:

Nine scatter plots of density, pressure, energy, x velocity, y velocity, z velocity, magnetic field in y, magnetic field in z, and psi vs x position in cells. The density plot shows a value of 1 jump to a value of 2.5 at x = 40 cells, followed by a jump to 3.9 at x = 140 cells and a drop to 3.85 at c = 150 cells. There is a final density drop to 1.0 at x = 225 cells. The pressure plot consists of a value of 1 which jumps to 155 at x = 40 cells. This value remains until x = 150, where it transitions to a value of x = 145. There is a final drop in pressure to 1.0 around x = 225 cells. From left to right, we see a fast shock followed by a slow rarfaction, contact discontinuity, slow shock, and fast shock..

We can compare this to the solution of Ryu and Jones, 1995:

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