A method of characteristics for computing the supersonic, nonequilibrium flow of a reacting and relaxing gas was formulated. The theory was specialized to the ideal dissociating gas of Lighthill and the procedures coded on the IBM 7094. Complete listings of the FORTRAN programs are provided together with instructions as to their use. As examples of the computation techniques, the flows over a wedge and cone were computed and described in detail. For both the wedge and the cone, there developed downstream from the vertex an entropy layer near the wall, a relaxation layer near the shock where the quantities change rapidly, and a near equilibrium layer in between. It was found that it is important to keep the size of the mesh small enough to adequately represent the relaxation layer if satisfactory convergence to the equilibrium state is to be obtained. (Author).

The method of characteristics for the supersonic axially symmetric or two-dimensional flow of Lighthill's ideal dissociating gas under thermodynamic equilibrium is formulated, for efficient calculation, by an electronic digital computer. The equations are simplified by the introduction of the streamline slope and the cotangent of the Mach angle as independent variables. Under this transformation, the coefficients in the characteristic differential equations become rational algebraic functions. Procedures for computing the flow conditions at the next downstream interior point and for computing the next downstream point along a solid boundary, along a shock wave, and along the axis are described in detail. A complete program coded in FORTRAN for the IBM 7094 computer is listed and instructions for its use are explained. (Author).

Since the appearance of computers, numerical methods for discontinuous solutions of quasi-linear hyperbolic systems of partial differential equations have been among the most important research subjects in numerical analysis. The authors have developed a new difference method (named the singularity-separating method) for quasi-linear hyperbolic systems of partial differential equations. Its most important feature is that it possesses a high accuracy even for problems with singularities such as schocks, contact discontinuities, rarefaction waves and detonations. Besides the thorough description of the method itself, its mathematical foundation (stability-convergence theory of difference schemes for initial-boundary-value hyperbolic problems) and its application to supersonic flow around bodies are discussed. Further, the method of lines and its application to blunt body problems and conical flow problems are described in detail. This book should soon be an important working basis for both graduate students and researchers in the field of partial differential equations as well as in mathematical physics.

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Chemical and vibrational nonequilibrium phenomena in steady inviscid flow fields are studied by the analysis of flow past curved boundaries. Possible alternative choices of the state variables to be used are considered. General features of the nonequilibrium flow are studied by examination of the mathematical properties of the nonlinear flow equations. An axisymmetric nonequilibrium flow of air through a supersonic nozzle is analyzed by means of numerical computations. The coupling effects between nonuniformity (across a nozzle section) and nonequilibrium, not taken into account in the quasi-one-dimensional flow approximation, are revealed by the present analysis.