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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 python.
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, ideal polytropic fluid. It is remarkable that this model yields exact, although algebraically complicated, analytical expressions for the fluid quantities. Kamm, Bolstad (RIP), & Timmes 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, singular and vacuum cases. In the standard, case a nonzero solution extends from the shock to the origin, where the pressure is finite. In the singular 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 venerable Sedov problem might appear to be an old solved problem. However, there is a paucity of papers that discuss all possible families of real solutions, in all common geometries, and address all the removable singularities. Jim Kamm's opus and David Book's slightly irreverant paper on generating Sedov solutions are worth reading. 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 hydrocode. In this paper we identify several new verification problems involving more challenging Sedov blast waves. Analytic and numerical solutions for verification purposes re discussed in this paper, this paper, and this paper. Standard, singular and vacuum solutions:
Sedov functions 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. Below are a few example plots of f (red; scaled material velocity), g (blue, scaled mass density), and h (green, scaled pressure) versus scaled distance λ; with γ and ω labeled.
Code verificaton efforts:
Density uniform 2D mesh:
Density 2D adaptive mesh:



