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Mader Verification Problem

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Contact: F.X.Timmes
my one page vitae,
full vitae,
research statement, and
teaching statement.
In this paper, this paper, and this paper, we discuss the analytic and numerical solutions for the Mader problem.

The simplest test of detonation is the one-dimensional gamma-law rarefaction wave burn, for which a slab of material is initiated 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 us for the detonation to travel 5 cm. The rich structure of a multi-dimensional detonation is absent in the one-dimensional test problem, and a simple rarefaction wave follows the detonation front (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 sonic there, and the tail of the rarefaction is halfway between the front and the piston.

The following code for the analytic solution is released to the public under LA-CC-05-101: rarefaction.f

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simple detonation
here are less-simple ones
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analytical and numerical
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convergence study
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evolution movie
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evolution movie


Density uniform mesh:
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density 200x200 cells
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density 400x400 cells
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density 800x800 cells
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density error 200x200 cells
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density error 400x400 cells
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density error 800x800 cells
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density asymmetry 200x200
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density asymmetry 400x400
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density asymmetry 800x800


Pressure uniform mesh:
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pressure 200x200 cells
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pressure 400x400 cells
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pressure 800x800 cells
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pressure error 200x200 cells
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pressure error 400x400 cells
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pressure error 800x800 cells
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pressure asymmetry 200x200
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pressure asymmetry 400x400
image
pressure asymmetry 800x800


Material Speed uniform mesh:
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speed 200x200 cells
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speed 400x400 cells
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speed 800x800 cells
image
speed error 200x200 cells
image
speed error 400x400 cells
image
speed error 800x800 cells
image
speed asymmetry 200x200
image
speed asymmetry 400x400
image
speed asymmetry 800x800


Density adaptive mesh:
image
density 200x200 cells
image
density 400x400 cells
image
density 800x800 cells
image
density error 200x200 cells
image
density error 400x400 cells
image
density error 800x800 cells


Pressure adaptive mesh:
image
pressure 200x200 cells
image
pressure 400x400 cells
image
pressure 800x800 cells
image
pressure error 200x200 cells
image
pressure error 400x400 cells
image
pressure error 800x800 cells


Material Speed adaptive mesh:
image
speed 200x200 cells
image
speed 400x400 cells
image
speed 800x800 cells
image
speed error 200x200 cells
image
speed error 400x400 cells
image
speed error 800x800 cells