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The focusing of very weak and slightly concave symmetrical shock waves is examined. The equation that describes this focusing is derived and the resulting similitude discussed. The initial conditions come from a formal matching of this nonlinear description with the linear solution. The maximum value of the pressure coefficient is shown to be proportional to the two-thirds power of both the initial strength of the wave front and a parameter characterizing its rate of convergence.

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A fully conservative numerical method for the computation of steady inviscid supersonic flow about general conical bodies at incidence is described. The procedure utilizes the potential approximation and implements a body conforming mesh generator. The conical potential is assumed to have its best linear variation inside each mesh cell; a secondary interlocking cell system is used to establish the flux balance required to conserve mass. In the supersonic regions the scheme is desymmetrized by adding artificial viscosity in conservation form. The algorithm is nearly an order of a magnitude faster than present Euler methods and predicts known results accurately and qualitative features such as nodal point liftoff correctly. Results are compared with those of other investigators.