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3a3 aaa arbitrary constants arbitrary parameters Author(s Axial node axial velocity boundary conditions bounded by nodes centered CFL condition COMPRESSIBLE FLUID MECHANICS compute conservation equations constraint term Contractor Report control volume Conventional numerical demonstrates the validity determined by equation diaphragm burst problem differencing scheme dyad element entropy formation equations 18 equations are satisfied equations of motion explicit FLUID MECHANICS DISCUSSION flux terms following fashion functional governing equations inequality constraint inlet integrated inviscid Jespus l-Bn Lagrange multipliers Law of Thermodynamics linear NASA negative pressures numerical analog Numerical analysis numerical solution ONE-DIMENSIONAL THEORY Performing Organization pressure distribution pressure or density PRINCIPLE FOR COMPRESSIBLE Report No3 result Robert Joel Prozan Second Law shock tube shown in figure sional Sponsoring Agency step subsequent discussion system entropy tube and diaphragm typical Unclassified unsteady flow value of 8n values of beta variational principle variational statement vector wave zero