wiki:MachStems

Version 13 (modified by ehansen, 10 years ago) ( diff )

Mach Stems


2D Stationary Clumps

This problem set up has bow shocks from two identical, stationary clumps. I test different gammas and different separation distances. To reduce computation, I am only using one clump with a reflecting wall on the lower r boundary to simulate the second clump's bow shock. I also only simulate ¼ of the clump due to symmetry. In the context of this problem, critical separation distance is equivalent to 2 times the critical radius.

Thinking in terms of critical radius versus critical angle can get confusing. Traditionally, we think of mach stem formation in terms of critical angle. Anything above this angle means a mach stem will form. The critical angle corresponds to a critical radius, but now we must remember that anything below this radius means a mach stem will form.

Below is a table of the resolutions used for all of the runs. These were determined by keeping the proportions of the domain constant and shooting for a minimum of 32 cells per clump radius. As a result of doing it this way, some runs will have higher resolution, but it basically stays between 32 and 38 cells per clump radius. For the 'lower r boundary' column, crit = critical, acrit = above critical, bcrit = below critical. Mach stems should form at crit and bcrit, but not at acrit.

gamma lower r boundary Base Grid (r,z) [cells] Domain Size (r,z) [cu] Cells / Rclump
1.6667 crit 12, 18 1.46, 2.19 32.88
1.6667 acrit 14, 21 1.66, 2.49 33.73
1.6667 bcrit 12, 18 1.26, 1.89 38.10
1.4 crit 12, 18 1.39, 2.085 34.53
1.4 acrit 14, 21 1.59, 2.385 35.22
1.4 bcrit 10, 15 1.19, 1.785 33.61
1.2 crit 12, 18 1.32, 1.98 36.36
1.2 acrit 14, 21 1.52, 2.28 36.84
1.2 bcrit 10, 15 1.12, 1.68 35.71
1.1 crit 12, 18 1.27, 1.905 37.80
1.1 acrit 12, 18 1.47, 2.205 32.65
1.1 bcrit 10, 15 1.07, 1.605 37.38


gamma = 1.6667

left boundary Image Movie
bcrit movie
crit movie
acrit movie


gamma = 1.4

movie


3D Runs

Run # Clumps Defining parameters Machine Frames (out of 50) Inclination Angles
A 2 d = 2.5, M = 7, 10 Gordon 0
B 2 d = 4.5, M = 7, 10 Gordon 44
C 2 d = 6.5, M = 7, 10 Gordon 0
D 2 d = 2.5, M = 7, 15 Stampede 34
E 2 d = 4.5, M = 7, 15 Stampede/Comet 27
F 2 d = 6.5, M = 7, 15 Stampede/Comet 45
G 3 d = 2.5, a = 30 BlueHive 22
H 3 d = 2.5, a = 60 BlueHive 49
I 3 d = 2.5, a = 90 BlueHive 39
J 3 d = 4.5, a = 30 BlueStreak 50
K 3 d = 4.5, a = 60 BlueStreak 50
L 3 d = 4.5, a = 90 BlueStreak 50
M 10 BlueStreak 50

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