HIGH-RESOLUTION CALCULATIONS IN GAS DYNAMICS

TWO APPROACHES ARE POSSIBLE FOR OBTAINING NUMERICAL SOLUTIONS TO STEADY FLOW PROBLEMS IN AERODYNAMICS. ONE MAY SOLVE THE UNSTEADY EQUATIONS (EITHER TIME ACCURATELY OR NOT)WITH AN INITIAL GUESS; OR, THE STEADY EQUATIONS MAY BE SOLVED DIRECTLY. FOR THOSE SITUATIONS (E.G., MISSILE AERODYNAMICS, REENTRY) FOR WHICH THE FLOW FIELD IS ENTIRELY SUPERSONIC, THE STEADY EQUATIONS THEMSELVES ARE HYPERBOLIC AND EXPLICIT (I.E., NO MATRIX INVERSIONS) MARCHING SCHEMES ARE POSSIBLE. THIS REDUCES THE COMPUTER PROBLEM BY A FULL DIMENSION. WE PROPOSE TO ADAPT VERSIONS OF THE SECOND-ORDER GODUNOV AND OTHER RELATED UPWIND SCHEMES FOR SUPERSONIC STEADY FLOW APPLICATIONS. THESE SCHEMES HAVE BEEN EXTENSIVELY USED IN UNSTEADY GAS DYNAMICS (AS WELL AS OTHER SYSTEMS OF HYPERBOLIC CONSERVATION LAWS SUCH AS OIL RESERVOIR SIMULATION) WITH SUBSTANTIAL SUCCESS DURING THE 1980'S. THE ALGORITHM WILL BE TESTED ON THE STEADY ANALOGUE OF THE PROBLEM OF (UNSTEADY) SELF-SIMILAR SHOCK WAVE REFLECTION. IN PARTICULAR, WE ARE INTERESTED IN RESOLVING THE QUESTION OF WHETHER OR NOT MACH REFLECTION MUST BE SIMPLE (OBSERVED EXPERIMENTALLY), OR MAY BE COMPLEX OR DOUBLE AS IN THE UNSTEADY CASE. THIS QUESTION IS OF INTEREST FOR THE COMPLEX GEOMETRICS IN INLET FLOW FIELDS.