Vectorization of Algorithms in Computational Fluid Dynamics on the CRAY-1 Vector Computer

TL;DRAbstract

Among computational fluid dynamicists the tremendous impact of MacCormack’s contributions to the development of computational tools for integrating the governing equations for inviscid and viscous flows is well recognized, and this is documented by numerous publications based on the use of his methods for integrating steady as well as time-dependent Euler and Navier-Stokes equations. Best known are MacCormack’s purely explicit predictor-corrector versions |1,2| of the two-level scheme of Lax and Wendroff. Explicit schemes are easily applied, and can, in general, be completely vectorized, but they have to satisfy severe stability conditions with respect to the marching step size. Such conditions are most stringent for viscous flows if the wall-normal, boundary-layer direction is to be resolved properly, with step sizes for turbulent flows of the order of 0.00005 times the characteristic length involved. For the explicit method to be stable in time-dependent calculations, the time-wise s

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