

Home Astronomy research Software Infrastructure: MESA FLASH STARLIB My codes White dwarf supernova: Colliding white dwarfs Merging white dwarfs Ignition conditions Metallicity effects Central density effects Detonation density effects Tracer particle burning Subsonic burning fronts Supersonic burning fronts W7 profiles Massive star supernova: Rotating progenitors 3D evolution ^{26}Al & ^{60}Fe ^{44}Ti, ^{60}Co & ^{56}Ni Yields of radionuclides Effects of ^{12}C +^{12}C SN 1987A light curve Constraints on Ni/Fe ratios An rprocess Compact object IMF Stars: PreSN variations MC white dwarfs SAGB Classical novae He shell convection Presolar grains He burn on neutron stars BBFH at 40 years Chemical Evolution: Hypatia catalog Zone models H to Zn Mixing ejecta γrays within 100 Mpc Thermodynamics & Networks Stellar EOS Reaction networks Protonrich NSE MC reaction rates Verification Problems: Validating an astro code SuOlson Cog8 Mader RMTV Sedov Noh Software instruments Presentations Illustrations Videos Bicycle adventures AAS Journals 2017 MESA Summer School ASU+EdX AST111x Teaching materials Education and Public Outreach 2016 NSF SI2 PI Workshop Contact: F.X.Timmes my one page vitae, full vitae, research statement, and teaching statement. 
This software instrument is
released to the public under LACC05101: sedov3.f
Jeremiah Moskal, working with Dr. Jared Workman, has ported/refactored the instrument into python, avaliable in this zip file. von Neumann (1941), Taylor (1941) and Sedov (1946) independently derived a selfsimilar description of the evolution of the blast wave arising from a powerful explosion in a cold, uniform density background (also see Bethe et al 1947). They treated the explosion as an instantaneous release of energy at a point and assumed that the background material through which the expanding blast sweeps behaves as an 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. In this paper, this paper, and this paper, we also discuss the analytic and numerical solutions for the Sedov problem. 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 to become 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. Expressions and techniques for the removal of the apparent singularities are described. 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. The constant density, spherically symmetric Sedov blast wave stalwart test case in the 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. Jim Kamm's opus and David Book's irreverant paper on generating Sedov solutions are worth reading. Standard, singular and vacuum solutions:
Plots of the Sedov functions 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 mesh: Density adaptive mesh: 


