Numerical Solutions of the Euler Equations for Steady Transonic Flow Past a Lifting Aerofoil
The well-known method of MacCormack is easily programmed, can be extended to two- and three-dimensional problems, and will capture shocks. However, it does have some bad features. The predictor equation assumes that the characteristics are always in one preselected direction at each point, though the corrector stage often cancels the resulting error. Near shocks, computed solutions frequently contain ‘wiggles’, spaced regularly along the mesh and clearly induced by the method. The results can depend greatly on the value of the local Courant-Friedrichs-Lewy (CFL) number. Also, the method cannot sort out incoming and outgoing waves at computational boundaries in subsonic flow; thus signals are reflected and wander about, unable to escape, and even when dissipation terms are added convergence to a steady flow is slowed down. It would be worthwhile to develop a method with the advantages of MacCormack’s method but without the drawbacks, and Phil Roe at RAE Bedford has shown how to obtain a very effective method for one-dimensional problems; the author at RAE Farnborough has borrowed many of his techniques and applied them to the problem of the title, and fuller details will be given in Ref 1 in due course.
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- 1.C.C.L. Sells: Solution of Euler equations for transonic flow past a lifting aerofoil. RAE Technical Report (to be published)Google Scholar
- 2.J.L. Steger and R.F. Warming: Flux vector splitting of the inviscid gasdynamic equations with application to finite difference methods. NASA Technical Memorandum 78605 (1978)Google Scholar