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1D Test 3

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evazlimen edited this page Jul 16, 2024 · 2 revisions

1D Test 3 (strong shock test)

This test is similar to the strong shock test but with only an initial pressure discontinuity. This shows the ability of a code to resolve contacts. Toro's Riemann solvers and numerical methods for fluid dynamics Sec. 6.3.3, test 3. The setup consists of a pressure of 1000 for 0 < x < 0.5 and 0.01 for 0.5 < x < 1.0. Gamma is set to 1.4 and density is 1.0 everywhere. This test was performed with the hydro build (cholla/builds/make.type.hydro) and Van Leer integrator. Full initial conditions can be found in cholla/src/grid/initial_conditions.cppunder Riemann().

Parameter file: (modified fromcholla/examples/1D/test_3.txt)

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

#
# Parameter File for test 3 (strong shock test)
# Parameters derived from Toro, Sec. 6.4.4, test 3
#

################################################
# 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=0.0
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=0.0
vy_r=0.0
vz_r=0.0
# pressure of right state
P_r=0.01
# location of initial discontinuity
diaph=0.5
# 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, with the leftmost plot showing the initial and the rightmost the final. The second and third rows are the same for pressure and velocity, respectively. 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 value of 1.0 for all x. The final density plot shows a value of 1.0 gradually decrease to 0.1 by x = 0.35, where it reamins constant until x = 0.7. Here it jumps to a value of 6 before dropping back down to a value of 1. The width of the spike is around 0.1. The density remains at 1 for the remainder of the grid. The intial pressure plot shows a value of 1000 for x between 0.0 and 0.5 and a value of 0.01 elsewhere. The final pressure plot shows a value of 1000 gradually decrease to 450 by x = 0.35. Here it remains approximately constant until x = 0.8 where it drops discontinuously to a value approaching zero. The initial velocity plot shows a value of 0.0 for all x. The final velocity plos shows a value of 0 from x = 0.0 to x = 0.05. It then increases to approximately 20 by x = 0.35, where it remains constant until x = 0.8, where it drops back to zero.

We see a contact discontinuity follow directly by a shock. This solution is in agreement with that of Toro test 3, shown below:

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