FOCUSING OF REFLECTED SHOCK-WAVES ANALYZED BY MEANS OF GEOMETRICAL SHOCK DYNAMICS

In the present work, a numerical scheme for the unsteady motion of shock waves in gases is developed based on Whitham's theory of geometrical shock dynamics (GSD). To investigate the effect of the initial shock strength on the shock reflection and diffraction on a wall, the two-dimensional focusing of cylindrical blast waves reflected from a concave elliptic wall is analyzed under various initial conditions. The results are compared with finite difference simulations based on the piecewise linear method (PLM) as well as with previous experimental results. It is found that geometrical shock dynamics is a practical and economical method to analyze the shock focusing process of the blast waves produced by exploding wires. Pressure changes along the major axis of the ellipse show good agreement when the present computations are compared with experimental results as well as with PLM simulations.