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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.
Noh's (1987) test case is a standard verification problem. A sphere of gas with a gamma-law equation of state is uniformly compressed, testing the ability to transform kinetic energy into internal energy, and the ability to follow supersonic flows. In the standard Noh problem, a cold gas is initialized with a uniform, radially inward speed of 1 cm s$^{-1}$. A shock forms at the origin and propagates outward as the gas stagnates. For an initial gas density of $\rho_0$ = 1 g cm$^{-3}$, the analytic solution in spherical geometry for $\gamma$ = 5/3 predicts a density in the stagnated gas, i.e., after passage of the outward moving shock, of 64 g cm$^{-3}$ .

Most hydrocode implementations produce anomalous "wall-heating" near the origin. As the shock forms at the origin the momentum equation tries to establish the correct pressure level. However, numerical dissipation generates entropy. The density near the origin drops below the correct value to compensate for the excess internal energy (e.g., Rider 2000). Thus, the density profile is altered near the origin while the pressure profile remains at the correct constant level in the post-shock region. See Gehmeyr, Cheng, & Mihalas (1997) for a remarkable exception. This article, this article, this article, and discuss analytic and numerical solutions for the Noh test case.

The tool in noh.tbz provide solutions as a function of time and position for the RMTV verification test case.

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analytical and numerical
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convergence study
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