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The simplest test of detonation is the one-dimensional, gamma-law equation of state,
rarefaction wave. Here a slab of material is ignited
on one side and a detonation propagates to the other side. For a
Chapman-Jouget detonation speed of 0.8 cm/s,
it takes 6.25 $\mu$s for the detonation to travel 5 cm.
The
rich
structure of a multi-dimensional
detonation is absent, and a simple rarefaction wave follows the detonation front
(e.g., Fickett & Davis 1979).
Expansion of material in the rarefaction depends on
the boundary condition where the detonation is initiated, which is
usually modeled as a freely moving surface or a moving piston. For
the Mader problem, a stationary piston is used. In this case, the
head of the rarefaction remains at the detonation front since the
flow is sub sonic, and the tail of the rarefaction is halfway between
the front and the piston.
This article,
this article,
and this article,
discuss analytic and numerical solutions for the Mader problem.
The tool in mader.tbz provide solutions as a function of time and position for the Mader verification test case.
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