## Conservative-variable Average States for Equilibrium Gas Multi-dimensional FluxesNational Aeronautics and Space Administration, Lewis Research Center, 1992 - Continuum mechanics - 46 pages |

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acoustic-wave average Ap Ap Ap associated average jacobian assumptions average density average eigenvalues average enthalpy average partial derivatives average sound speed average state q chain rule classical thermodynamic coincide computed Consequently conservation variables constitutes the average-state continuity equation contravariant flux convection average correspond curvilinear coordinate denotes density and momentum depends derivations algebraically derivatives of pressure detailed in Section developed differential dp dp eigenvalue consistency theorem eigenvalue set eigenvector matrix energy equation exact average flux difference resolution flux variation Furthermore gas average geometric solution projection Hence ideal-gas average identically satisfied integration paths internal energy left and right Liou's Mach number mass specific internal mean value theorem negative eigenvalues pointwise pressure derivatives pressure jacobian derivatives pressure variation relation procedures real gas revert sound speed expressions sound speed squared speed of sound supersonic flow variable average variation and average vector decomposition Vinokur Whereupon yields