On the propagation of a weak shock front - Theory and application

A shock manifold equation is obtained for a system of hyperbolic equations expressed in conservation form to model the kinematics of a weak shock front in a gas. The theory is applied to the two-dimensional analysis of the shock produced by the abrupt introduction of a cylinder in a compressible flow. The calculations indicate that the nonlinear wave front propagates faster upstream than the linear wave front. The shock front will be midway between the linear and nonlinear wave fronts and progress with their mean velocity. The nonlinear flow will not be observable experimentally but is accounted for by the model.