Detonation of a heterogeneous explosive charge in a cylindrical tube. At the shock front a special treatment is done to partition the shock energy among the various components. At the sonic surface generalized CJ conditions are fulfilled. At material interfaces equal normal velocity and pressures are matched. All these interface conditions are considered in a unique flow model of heterogeneous material consisting in a hyperbolic system of equations with relaxation. Details are given in Petitpas et al. (2009) and Schoch et al. (2013).