Shock-Fitting using Hamilton-Jacobi Solver for High Order Solutions of Curved Detonation

Detonation front shape and phase speed are characteristic properties used to experimentally quantify the performance of High Explosives (HEs). Reactive burn models such as AWSD are also calibrated using these shot data as collected from charges in multiple standard geometries. Thus, HE simulation and calibration require accurate solutions at the propagating detonation front. Shock capturing and adaptive mesh refinement methods are limited to first order convergence in approximating such discontinuous solutions. Shock-fitting is a technique which effectively removes the lead-shock discontinuity, again making high order convergence possible. Here a new variation of shock-fitting method is presented which directly solves the Hamilton-Jacobi equation describing the detonation front, yielding the shock shape and speed to high order. The high order convergence of the method is verified using an exact solution for a polytropic gas with a depletion reaction rate. Solution validation is made using diameter effect data for a number of conventional HEs. Comparison with previous variations of the shock-fit algorithm are also given.