Various numerical schemes are developed to calculate the motion of shock waves in gases based on Whitham's theory of geometrical shock dynamics. The basic numerical scheme is used to study the propagation of two-dimensional shock waves along walls and in channels, and the self-focusing of initially curved shock- fronts. This scheme is extended to treat shock wave motion in non-uniform media. The extended scheme is used to examine shock wave refraction at both planar and curved interfaces separating gases with different properties. Precursor-irregular refraction patterns are obtained using geometrical shock dynamics. A general numerical scheme designed to propagate a shock surface in three dimensions is presented. Three-dimensional shock focusing and shock propagation in a curved pipe are considered primarily to demonstrate the use of the three-dimensional numerical scheme. The reflection of planar shock waves from curved walls is studied. The motion of the shock is determined using the combined theories of regular reflection and geometrical shock dynamics. A numerical scheme based on the combined theories is discussed. The numerical scheme is used to calculate the reflection and subsequent focusing of weak planar shock waves. Some of the present results are compared with other solutions to the equations of geometrical shock dynamics obtained using different methods. Recent experimental investigations are discussed and compared with our results calculated using geometrical shock dynamics.
