#
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.