GENESIS—GEneralized Nonlinear Extension of Surface Integral Schemes—offers the prospect of extending existing 3-D panel codes, originally developed for linear flows over complex configurations, to the general re´gime of flows governed by the unsteady Euler equation—without significant increases in computational time or resources. The boundary representation of a shock discontinuity exploits its causal link with conditions at the sonic point to suppress, non-dissipatively, the physically-impossible formation of an expansion shock. Three approaches are described, two approximate and one nominally exact, for solving the transonic Euler equation on conventional computers; some 2-D transonic results are presented, obtained on a PC in about one second.

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