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Scramjet Project
Uncertainty Quantification
Errors in Numerical Solutions of Shock Physics Problems
PowerPoint presentation from dissertation defense
(with the constant pressure boundary condition driving a Mach
2 Shock into the radial domain)
Animation |
Mesh Size |
Offset |
Perturbation |
200X400 |
no |
single mode |
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200X400 |
yes |
single mode |
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400X800 |
no |
single mode |
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400X800 |
yes |
single mode |
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800X1600 |
no |
single mode |
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800X1600 |
yes |
single mode |
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100X200 |
no |
random |
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100X200 |
yes |
random |
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200X400 |
no |
random |
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200X400 |
yes |
random |
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400X800 |
no |
random |
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400X800 |
yes |
random |
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800X1600 |
no |
random |
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800X1600 |
yes |
random |
Above are
LOG-DENSITY animations for implosion simulations in a two-dimensional
geometry with two materials: Tin (heavy, outside of contact) and Lucite
(light, inside of contact). The inner circle is the material boundary while the
outer circle is set as a constant-pressure boundary.
A Mach 2 shock was used in these
simulations.
The stopping time for those runs was set
to t = 80, at which time the driven shock has crossed the contact
interface, hit the origin and produced a reflected shock
which crosses the interface and eventually reaches the outer boundary.
The chaotic mixing of Tin and Lucite
(respectively, the heavy and light materials) was produced by the driven
and reflective shocks.
Below are the L-1 norms of
the differences (errors) between successive grid levels.
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