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Artificial Mass Concept and Transonic Viscous Flow Equation,
TEXAS UNIV AT AUSTIN DEPT OF AEROSPACE ENGINEERING AND ENGINEERING MECHANICS
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By varying the grid clustering on the surface of an airfoil, it was observed that symmetric shocked solutions develop with a nonunique shock strength and location when numerically solving the full potential equation. It is shown analytically that the conventional form of artificial density or viscosity produces a number of truly nonlinear terms which are suspected to be the cause of the nonuniqueness for all the finite grid sizes. A concept of artificial mass flow is shown to be suitable for analytically evaluating a new exact form of the switching function that eliminates all the nonlinear terms for any value of the local Mach number. The resulting expanded full potential equation then becomes a third order partial differential equation of permanently parabolic type resembling Sichels transonic viscous flow equation. Consequently, our expanded full potential equation does not require the introduction of the customarily-used artificial time concept. Author
APPROVED FOR PUBLIC RELEASE