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1D Stationary

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evazlimen edited this page Jul 22, 2024 · 2 revisions

1D Stationary Contact

This test initializes a stationary contact. Parameters derived from Toro's Riemann solvers and numerical methods for fluid dynamics Sec. 6.4, test 5. The setup consists of a pressure of 1000 for 0 < x < 0.8 and 0.01 for 0.8 < x < 1.0. Density and velocity are equal on both sides of the contact with values of 1.0 and -19.59745, respectively. Gamma is set to 1.4. This test was performed with the hydro build (cholla/builds/make.type.hydro). Full initial conditions can be found in cholla/src/grid/initial_conditions.cppunder Riemann().

Important: This test must be run with diode boundaries disabled in order to perform as expected (thank you @alwinm!). This branch also uses the Van Leer integrator.

Parameter file: (modified fromcholla/examples/1D/stationary.txt)

Modified to add yl_bcnd, yu_bcnd, zl_bcnd, and zu_bcnd=0

#
# Parameter File for Toro test 5, a stationary contact.
# Parameters derived from Toro, Sec. 6.4.4, test 5
# Same as test 3a from Liska, 2003.
#

################################################
# number of grid cells in the x dimension
nx=100
# number of grid cells in the y dimension
ny=1
# number of grid cells in the z dimension
nz=1
# final output time
tout=0.012
# time interval for output
outstep=0.012
# 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=0
yu_bcnd=0
zl_bcnd=0
zu_bcnd=0
# path to output directory
outdir=./

#################################################
# Parameters for 1D Riemann problems
# density of left state
rho_l=1.0
# velocity of left state
vx_l=-19.59745
vy_l=0.0
vz_l=0.0

# pressure of left state
P_l=1000
# density of right state
rho_r=1.0
# velocity of right state
vx_r=-19.59745
vy_r=0.0
vz_r=0.0
# pressure of right state
P_r=0.01
# location of initial discontinuity
diaph=0.8
# value of gamma
gamma=1.4

Upon completion, you should obtain two output files. The initial and final density, pressure, and velocity (in code units) of the solution is shown below (pink dots) plotted over the exact solution (purple line). Examples of how to extract and plot data can be found in cholla/python_scripts/plot_sod.ipynb.
Three rows of two scatter plots side by side. The first row shows density vs x position, the second row shows pressure vs x position, and the third row shows velocity vs position. In all rows, the first plot has the text 't = 0.00' in the upper right corner while the second plot has the text 't = 0.012' in the upper right corner. The plots of the first column are shown with pink dots while the plots of the second column have pink dots plotted over a purple line. In all cases, the pink dots match the shape of the purple line, albeit imperfectly. The initial density plot shows a constant value of 1 for all x while the final density plot shows a value of 1.0 remain constant until x = 0.1, at which it decreases to a value of 0.6 by x = 0.4. Here it remains approximately constant until it spikes to a value of 6 around x = 0.8. The width of the spike is less than 0.1 in x. From x = 0.9 to x = 1.0 density is constant at 1. The initial pressure plot shows a constant value of 1000 for x between 0.0 and 0.8 and a value of 0.01 for x between 0.8 and 1.0. The final pressure plot shows a value of 1000 until x = 0.1. Here it gradually decreases to a value of 450 at x = 40.4, where it remains constant until x = .85 cells. It abruptly drops to almost zero and stays there for the remaining 0.15 in x. The initial velocity plot shows a value of -19.59745 for all x. The final velocity plot shows a value of -19.59745 for x between 0.0 and 0.1, at which point the velocity decreases towards zero, which it reaches at x = 0.4. It remains at zero until x = 0.85, where it drops back to -19.59745.

We see a stationary contact at x = 0.8. The width of the contact is not fully resolved. With the diode disabled,this solution matches that of Liska and Wendroff 2003 (http://www-troja.fjfi.cvut.cz/~liska/CompareEuler/compare8-bw.pdf).

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