The Method of Characteristics for Three-Dimensional Problems in Gas Dynamics

Abstract

Although both the Godunov and BVLR methods for solving compressible flow problems in three dimensions use finite difference formulas in rectangular networks their foundations rest on the properties of characteristics of the governing equations. Both before and during the development of these methods, over the past twenty five years, a series of methods of characteristics, as such, have been proposed for three dimensional problems. Many of these compete with finite difference techniques, especially when applied to such problems as unsteady transonic flow, and it is appropriate to include a survey of such methods here. They may be classified under four headings:

• 1) Methods based entirely on bicharacteristics (Thornhill (1952), Fowell (1961), Butler (1960), Ransom et al. (1970)).

• 2) Methods based on two bicharacteristic families and one noncharacteristic family (Coburn and Dolph (1949), Holt (1956)).

• 3) Optimal methods of type 2) (Bruhn and Haack (1958), Schaetz (1961)).

• 4) Methods based on characteristic lines not in the bicharacteristic direction (Albrecht and Urich (1961). Sauer (1962)).