Cococubed.com Noh Verification Problem
Home Astronomy research   Software Infrastructure:      MESA      FLASH-X      STARLIB      MESA-Web      starkiller-astro      My instruments   White dwarf pulsations:      12C(α,γ) & overshooting      Probe of 12C(α,γ)16O      Impact of 22Ne      Impact of ν cooling      Variable white dwarfs      MC reaction rates      Micronovae      Novae   White dwarf supernova:      Stable nickel production      Remnant metallicities      Colliding white dwarfs      Merging white dwarfs      Ignition conditions      Metallicity effects      Central density effects      Detonation density      Tracer particle burning      Subsonic burning fronts      Supersonic fronts      W7 profiles   Massive stars:      Pop III with HST/JWST      Rotating progenitors      3D evolution to collapse      MC reaction rates      Pre-SN variations   Massive star supernova:      Yields of radionuclides      26Al & 60Fe      44Ti, 60Co & 56Ni      SN 1987A light curve      Constraints on Ni/Fe      An r-process      Effects of 12C +12C   Neutron Stars and Black Holes:      Black Hole spectrum      Mass Gap with LVK      Compact object IMF      He burn neutron stars   Neutrino Emission:      Neutrino emission from stars      Identifying the Pre-SN      Neutrino HR diagram      Pre-SN Beta Processes      Pre-SN neutrinos   Stars:      Hypatia catalog      SAGB stars      Nugrid Yields I      He shell convection      BBFH at 40 years      γ-rays within 100 Mpc      Iron Pseudocarbynes   Pre-Solar Grains:      C-rich presolar grains      SiC Type U/C grains      Grains from massive stars      Placing the Sun      SiC Presolar grains   Chemical Evolution:      Radionuclides in 2020s      Zone models H to Zn      Mixing ejecta   Thermodynamics, Opacities & Networks      Radiative Opacity      Skye EOS      Helm EOS      Five EOSs      Equations of State      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 AAS Journals    2025 AAS YouTube    2025 AAS Peer Review Workshops 2025 ASU Energy in Everyday Life 2025 MESA Classroom Other Stuff:    Bicycle Adventures    Illustrations    Presentations Contact: F.X.Timmes my one page vitae, full vitae, research statement, and teaching statement.	Noh's (1987) test case is a standard verification problem. A sphere of gas with a gamma-law equation of state is uniformly compressed, testing the ability to transform kinetic energy into internal energy, and the ability to follow supersonic flows. In the standard Noh problem, a cold gas is initialized with a uniform, radially inward speed of 1 cm s$^{-1}$. A shock forms at the origin and propagates outward as the gas stagnates. For an initial gas density of $\rho_0$ = 1 g cm$^{-3}$, the analytic solution in spherical geometry for $\gamma$ = 5/3 predicts a density in the stagnated gas, i.e., after passage of the outward moving shock, of 64 g cm$^{-3}$ . Most hydrocode implementations produce anomalous "wall-heating" near the origin. As the shock forms at the origin the momentum equation tries to establish the correct pressure level. However, numerical dissipation generates entropy. The density near the origin drops below the correct value to compensate for the excess internal energy (e.g., Rider 2000). Thus, the density profile is altered near the origin while the pressure profile remains at the correct constant level in the post-shock region. See Gehmeyr, Cheng, & Mihalas (1997) for a remarkable exception. This article, this article, this article, and discuss analytic and numerical solutions for the Noh test case. The tool in noh.tbz provide solutions as a function of time and position for the RMTV verification test case. analytical and numerical convergence study