Unsteady Three-Dimensional Flow Theory Via Material Functions,
WATERLOO UNIV (ONTARIO)
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A new Lagrangian formulation for unsteady three dimensional supersonic inviscid flow over rigid bodies is developed. The continuity equation is eliminated by the use of material functions, a generalization of the stream functions for steady flow. This is followed by a transformation to new independent variables, three of which are these material functions. The fourth variable is a Lagrangian time distinct from the Eulerian time. The simultaneous use of both Lagrangian and Eulerian time allows the problem of flow with shock wave to be reduced to a fixed boundary one. In the Newtonian limit it is found possible to obtain analytic solutions for various body shapes.