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- 1989 (45) (remove)
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- English (45) (remove)
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Keywords
Today the most accurate and cost effective industrial codes used in aircraft design are based on the full potential equation coupled with boundary layer equations. However, these are not capable to solve complicated three-dimensional problems of vortical flows and shocks. On the other hand Euler and Navier-Stokes codes are too expensive and not accurate enough for design purposes, especially in regard of drag and interference prediction. The reasons for these deficiencies are investigated and a way to overcome them by future developments is demonstrated.
The nonlinear scalar constitutive equations of gases lead to a change in sound speed from point to point as would be found in linear inhomogeneous (and time dependent) media. The nonlinear tensor constitutive equations of solids introduce the additional local effect of solution dependent anisotropy. The speed of a wave passing through a point changes with propagation direction and its rays are inclined to the front. It is an open question whether the widely used operator splitting techniques achieve a dimensional splitting with physically reasonable results for these multi-dimensional problems. May be this is the main reason why the theoretical and numerical investigations of multi-dimensional wave propagation in nonlinear solids are so far behind gas dynamics. We hope to promote the subject a little by a discussion of some fundamental aspects of the solution of the equations of nonlinear elastodynamics. We use methods of characteristics because they only integrate mathematically exact equations which have a direct physical interpretation.