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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.



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