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Noh 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 Noh problem.

The Noh problem (Noh 1987) is a standard verification problem for hydrocodes. A sphere of a gamma-law gas is uniformly compressed, testing a codes ability to transform kinetic energy into internal energy, and the ability to follow supersonic flows. In the Noh problem, a spherical, cold ideal gas is initialized with a uniform, radially inward speed of 1 cm/s. A shock forms at the origin and propagates outward as the gas stagnates. For an initial gas density of 1 g/cc, the analytic solution for gamma = 5/3 predicts a density in the stagnated gas, after passage of the outward shock, of 64 g/cc. Most hydrodynamics codes, produce anomalous "wall-heating" near the origin. This heating causes premature stagnation, with densities much lower than predicted in the centermost cells.

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

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3d noh
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analytical and numerical
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convergence study
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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
image
pressure error 800x800 cells
image
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
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speed error 200x200 cells
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speed error 400x400 cells
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speed error 800x800 cells


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