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This software instrument is released to the public under LACC05101:
sedov3.f.zip.
Jeremiah Moskal and Jared Workman
have ported/refactored this instrument to sedov_python.zip.
von Neumann (1941), Taylor (1941), Sedov (1946), and Bethe et al (1947) derived a selfsimilar description of the evolution of a blast wave arising from a point explosion in a cold, uniform density, polytropic fluid. It is remarkable that this model yields exact, although algebraically complicated, analytical expressions for the fluid quantities. The venerable Sedov problem might appear to be an old solved problem. However, there is a paucity of openknowledge software instruments that discuss 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 ρ=ρ_{0}r^{ω} in planar, cylindrical or spherical geometry for the standard, transitional, and vacuum cases. Jim Kamm's article and David Book's slightly irreverant paper are also worth reading. 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. 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 several, more challenging, Sedov blast waves. 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. Although the Sedov functions are analytic, they appear singular for various combinations of parameters and lower limits of integration. All six of these singularities are removable; they are a consequence of the way the solution is formulated. These four functions are shown below. Spherical geometry: Cylindrical geometry: Planar geometry: Energy Integral:
Verification efforts:
Density uniform 2D mesh:
Density 2D adaptive mesh:



