Cococubed.com Mader Verification Problem
Home Astronomy research   Software Infrastructure:      MESA      FLASH      STARLIB      MESA-Web      starkiller-astro      My instruments   White dwarf supernova:      Remnant metallicities      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      26Al & 60Fe      44Ti, 60Co & 56Ni      Yields of radionuclides      Effects of 12C +12C      SN 1987A light curve      Constraints on Ni/Fe ratios      An r-process   Neutron Stars and Black Holes:      Black Hole Mass Gap      Compact object IMF   Stars:      Neutrino HR diagram      Pulsating white dwarfs      Pop III with JWST      Monte Carlo massive stars      Neutrinos from pre-SN      Pre-SN variations      Monte Carlo white dwarfs      SAGB stars      Classical novae      He shell convection      Presolar grains      He burn on neutron stars      BBFH at 40 years   Chemical Evolution:      Iron Pseudocarbynes      Radionuclides in the 2020s      Hypatia catalog      Zone models H to Zn      Mixing ejecta      γ-rays within 100 Mpc   Thermodynamics & Networks      Stellar EOS      12C(α,γ)16O Rate      Proton-rich NSE      Reaction networks      Bayesian reaction rates   Verification Problems:      Validating an astro code      Su-Olson      Cog8      Mader      RMTV      Sedov      Noh Software instruments Presentations Illustrations cococubed YouTube Bicycle adventures Public Outreach Education materials 2022 ASU Solar Systems Astronomy 2022 ASU Energy in Everyday Life AAS Journals AAS YouTube 2022 Earendel, A Highly Magnified Star 2022 TV Columbae, Micronova 2022 White Dwarfs and 12C(α,γ)16O 2022 MESA in Don't Look Up 2022 MESA Marketplace 2022 MESA Summer School 2022 MESA Classroom 2021 Bill Paxton, Tinsley Prize Contact: F.X.Timmes my one page vitae, full vitae, research statement, and teaching statement.	The simplest test of detonation is the one-dimensional, gamma-law equation of state, rarefaction wave. Here a slab of material is ignited on one side and a detonation propagates to the other side. For a Chapman-Jouget detonation speed of 0.8 cm/s, it takes 6.25 $\mu$s for the detonation to travel 5 cm. The rich structure of a multi-dimensional detonation is absent, and a simple rarefaction wave follows the detonation front (e.g., Fickett & Davis 1979). Expansion of material in the rarefaction depends on the boundary condition where the detonation is initiated, which is usually modeled as a freely moving surface or a moving piston. For the Mader problem, a stationary piston is used. In this case, the head of the rarefaction remains at the detonation front since the flow is sub sonic, and the tail of the rarefaction is halfway between the front and the piston. This article, this article, and this article, discuss analytic and numerical solutions for the Mader problem. The tool in mader.tbz provide solutions as a function of time and position for the Mader verification test case. simple detonation here are less-simple ones