

Home Astronomy research Software instruments Stellar equation of states EOS with ionization EOS for supernovae Chemical potentials Stellar atmospheres Voigt Function Jeans escape Polytropic stars Cold white dwarfs Adiabatic white dwarfs Cold neutron stars Stellar opacities Neutrino energy loss rates Ephemeris routines FermiDirac functions Polyhedra volume Plane  cube intersection Coating an ellipsoid Nuclear reaction networks Nuclear statistical equilibrium Laminar deflagrations CJ detonations ZND detonations Fitting to conic sections Unusual linear algebra Derivatives on uneven grids Pentadiagonal solver Quadratics, Cubics, Quartics Supernova light curves Exact Riemann solutions 1D PPM hydrodynamics Hydrodynamic test cases Galactic chemical evolution Universal twobody problem Circular and elliptical 3 body The pendulum Phyllotaxis MESA MESAWeb FLASH Zingale's software Brown's dStar GR1D code Iliadis' STARLIB database Herwig's NuGRID Meyer's NetNuc Presentations Illustrations cococubed YouTube Bicycle adventures Public Outreach Education materials AAS Journals AAS Youtube 2020 Celebration of Margaret Burbidge 2020 Digital Infrastructure 2021 MESA Marketplace 2021 MESA Summer School 2021 ASU Solar Systems 2021 ASU Energy in Everyday Life Contact: F.X.Timmes my one page vitae, full vitae, research statement, and teaching statement. 
Given (i) a fuel's temperature, density and composition and (ii) that the fuel's ashes are in their equilibrium state (e.g., NSE in the nuclear case), then the ChapmanJouget (CJ; 1890) detonation solution follows from solving the the mass and momentum equation (which defines the "Rayleigh line" ; see illustration below) $$ (P_2  P_1)  (v_2 \rho_2)^2 \cdot (v_1  v_2) = 0 \label{rayleigh} \tag{1} $$ together with the energy equation (which defines the "Hugoniot curve"; see illustration) $$ E_1 + q_{\rm nuc}  E_2 + \dfrac{1}{2} (P_1 + P_2) (v_1  v_2) = 0 \label{hugoniot} \tag{2} $$ where $P$ is the pressure, $\rho$ is the density, $v$ is the material speed, $E$ is the specific internal energy, and $q_{\rm nuc}$ is the energy released by burning in going from the unshocked upstream material (subscript 1) to the final postshock downstream material (subscript 2). These two algebraic equations are to be solved simultaneously with the two algebraic equations for the postshock NSE composition. This is a fourdimensional root find, but it can be done efficiently as two nested twodimensional root finds. The CJ solution tells you the (i) speed of the detonation and (ii) the thermodynamics of the ashes. The CJ solution doesn't tell you the (a) the width of the fueltoash region, (b) the spatial variations of the variables, or (c) if the solution is a selfsustaining detonation. The tool in cjdet.tar.xz generates CJ solutions using the helmholtz equation of state and relevant parts of the torch network. It will also compute the strong and weak solutions if one chooses to drive the system at a userspecified Mach number. If one wants what a ChapmanJouget solution doesn't tell you, a ZND detonation might.



Please cite the relevant references if you publish a piece of work that use these codes, pieces of these codes, or modified versions of them. Offer coauthorship as appropriate. 
