

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 Hotter white dwarfs Cold neutron stars Stellar opacities Neutrino energy loss rates Ephemeris routines FermiDirac functions Galactic chemical evolution Coating an ellipsoid Universal twobody problem 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 Verification problems Plane  cube Intersection Phyllotaxis The pendulum Circular and elliptical 3 body MESA MESAWeb FLASH Zingale's software Brown's dStar GR1D code Iliadis' STARLIB database Herwig's NuGRID Meyer's NetNuc Presentations Illustrations Videos Bicycle adventures AAS Journals 2017 MESA Marketplace 2017 MESA Summer School 2017 ASU+EdX AST111x Teaching materials Education and Public Outreach Contact: F.X.Timmes my one page vitae, full vitae, research statement, and teaching statement. 
Given 1) the fuel's temperature, density and composition and 2) that the ashes exist in their equilibrium state (e.g., NSE in the nuclear case), then the ChapmanJouget (1890) detonation solution follows from solving the the mass and momentum "rayleigh line" equation $$ (P_2  P_1)  (v_2 \rho_2)^2 \cdot (v_1  v_2) = 0 \label{rayleigh} \tag{1} $$ together with the energy "hugoniot" equation $$ E_1 + q_{\rm nuc}  E_2 + \dfrac{1}{2} (P_1 + P_2) (v_1v_2) = 0 \label{hugoniot} \tag{2} $$ 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 euqations are to be solved simultaneously with the two algebraic equations for the postshock equilibrium composition (NSE). This is a fourdimensional root find, but it can be done efficiently as two nested twodimensional root finds. The CJ solution tells you the (1) speed of the detonation and (2) the thermodynamics of the ashes. The CJ solution doesn't tell you the (1) the width of the fueltoash region, (2) the spatial variations of the variables, and (3) if the solution is a selfsustaining detonation. The instrument in public_cjdet.tbz generates CJ detonation solutions. It will also compute the strong and weak detonation solutions if one chooses to drive the detonation at a userspecified Mach number. If one wants what the 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. 
