Recent Contributions to the Method of Characteristics for Three-Dimensional Problems in Gas Dynamics,

摘要

The numerical method of characteristics for problems in three or more independent variables are reviewed. Particular emphasis is laid on recent methods developed in Germany;notably the optimal characteristic method of Bruhn + Haack and Schaetz,and the near characteristics method of Sauer. In all these methods,difference equations are established in their most compact form and,at each point,all outer directional derivatives are in one plane. In Sauer's method,this plane is always parallel to a fixed plane. The methods are all derived rigorously and satisfy conditions of equivalence,uniqueness,and convergence. The optimal characteristics method has been applied very successfully to the problem of unsteady flow through a Laval nozzle. (Modified author abstract)