Computation of reactive duct flows in external fields

A GRP-scheme is introduced for the numerical integration of the Euler system of equations of compressible reactive flow in a duct of variable cross section, subject to an external potential. The GRP (generalized Riemann problem) scheme is based on an analytic solution of the GRP at jump discontinuities. It is a second-order scheme generalizing the first-order Godunov scheme, having the property of high resolution of shocks and other discontinuities. Some numerical examples are considered, including an infinite spherical reflected shock, a spherical blast wave and gas collapse under an external potential.