The Calculation and Accuracy of Shock Wave Propagation Using Geometrical Shock Dynamics

Don Schwendeman (RPI)

Geometrical shock dynamics is an approximate theory for the propagation of shock waves in gases. The theory is based on an approximation of the Euler equations in which the motion of the leading shock is determined explicitly. The equations of the geometrical shock dynamics are analogous to those for steady, supersonic, potential flow with a particular choice of the density-speed relation. Several numerical methods for the calculation of the shock waves within the approximate theory will be discussed. Numerical results will be presented for shock propagation in channels and for converging cylindrical and spherical shocks. The channel problem is used to compare the shockfronts calculated using the approximate theory with those obtained from a corresponding calculation of the full Euler equations. Converging cylindrical and spherical shocks are calculated to analyze their stability.