SHOCK FITTING AND NUMERICAL MODELING OF DETONATION WAVES MUHAMMAD AKRAM and FARHAD ALI ∗ Dr. A. Q. Khan Research Laboratories P.O. Box 502, Rawalpindi, Pakistan ∗ E-mail: ctrd@paknet2.ptc.pk Received 17 June 1997 Revised 7 August 1997 Numerical modelling of detonation using shock fitting is described in detail. A complete set of jump conditions that hold across the detonation front is presented in a simple form. Validity and accuracy of the model has been established by comparison with published results and results of another model utilizing the method of integral relations. A brief description of the later model is given to highlight its validity and limitations. Keywords : Detonation; Conservation Laws; Jump Conditions; Shock Fitting; Integral Relations. 1. Introduction A detonation wave is a supersonic shock wave with which is associated the release of heat energy and conversion of the explosive (whether gaseous, fluid or solid) to prod- uct gases and hence is usually modeled by chemically reacting compressible fluid flow equations. Compressible fluid flows having shocks and other discontinuities, like interfaces and gradient discontinuities, are numerically modeled by a variety of methods but the most popular amongst them are the shock capturing and shock fit- ting procedures. In shock capturing, the governing partial differential equations are solved first, ignoring all discontinuities, using a diffusive numerical scheme and then the solution is corrected using some form of filtering. 1−3 Shock fitting is an explicit way of discontinuity tracking in which the conservation/balance laws are applied in discrete form, known as jump conditions, in the vicinity of the discontinuity treat- ing it as a moving internal boundary and the normal flow equations are solved in the remaining domain. The jump conditions, normally referred to as the Rankine Hugoniot relations, can be found in standard texts on fluid dynamics e.g., in Refs. 4 and 5 etc. Their use to track discontinuities in computational models have received great attention in the works of Moretti 6,7 and Richtmyer and Morton. 8 See also Neef and Hechtman, 9 Shubin, 10 Chern, 11 Henshaw, 12 and Sternberg and Hurwitz. 13 For perfect gases, Rankine Hugoniot relations give a closed set of algebraic equations 7 but in general physical situations these relations provide a set in which the num- 1193