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Sedov Blast Wave
Verification Problem

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Contact: F.X.Timmes
my one page vitae,
full vitae,
research statement, and
teaching statement.
The tool sedov.tbz calculates Sedov solutions. Jeremiah Moskal and Jared Workman have ported/refactored this instrument to sedov_python.zip.

The venerable Sedov problem might appear to be an old solved problem. However, there is a paucity of open-knowledge software instruments that find all possible families of real solutions, in all common geometries, and address all the removable singularities. In this article we describe the generation of robust numerical solutions for a Sedov blast wave propagating through a density gradient $\rho = \rho_0 r^{-\omega}$ in planar, cylindrical or spherical geometry for the standard, transitional, and vacuum cases. In the standard case a nonzero solution extends from the shock to the origin, where the pressure is finite. In the transitional case a nonzero solution extends from the shock to the origin, where the pressure vanishes. In the vacuum case a nonzero solution extends from the shock to a boundary point, where the density vanishes. See Jim Kamm's article and David Book's slightly irreverant article.

The constant density, spherically symmetric Sedov blast wave is a stalwart test case for verification of hydrodynamic codes. However, it is not a particularily difficult test for a modern shock capturing hydrocode. In this article we identify more challenging Sedov blast waves for hydrocode verification purposes. Analytic and numerical solutions for verification purposes are discussed in this article, this article, and this article.

Four Sedov functions describe the spatial variation of density, material speed, and pressure with distance at any point in time:

Spherical geometry:
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Cylindrical geometry:
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Planar geometry:
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Energy Integral:
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Some verification efforts:
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