The Efficient Use of Vector Computers with Emphasis on Computational Fluid Dynamics pp 71-92 | Cite as

# Simulating 3D Euler Flows on a CYBER 205 Vector Computer

## Summary

A computational method for solving the 3D Euler equations is studied. The method is based upon an upwind flux-difference splitting scheme by Osher, exhibiting an implicit mechanism for numerical viscosity, in connection with an explicit time-marching finite-volume technique. The computer program is developed to run efficiently on both a scalar computer and the CYBER 205 vector computer. Demands made by the necessity of vectorizability of the code, on algorithm, data-structuring, and the code itself, are. discussed. Also, the large data sets involved in 3D calculations, appear to impose severe claims on central-memory size, I/O devices and line connections.

The method is tested for a transonic and supersonic quasi-two-dimensional channel flow. The Euler model is found to give an accurate simulation of aerodynamic phenomena in the channel.

## Keywords

Clock Cycle Hyperbolic System Contact Discontinuity Simple Wave Riemann Solver## Preview

Unable to display preview. Download preview PDF.

## References

- [1]Lax, P.D.: “Hyperbolic systems of conservation laws and the mathematical theory of shock waves”, Reg. Conf. Series in Applied Math., Siam 1973, no. 11.zbMATHCrossRefGoogle Scholar
- [2]Harten, A., Lax, P.D., Leer, B. van: “On upstream differencing and Godunov-type schemes for hyperbolic conservation laws”, Siam review no. 25.1, (1983).Google Scholar
- [3]Osher, S., Solomon, F.: “Upwind difference schemes for hyperbolic systems of conservation laws”, Math, of Comp., Vol. 38 (1982) pp. 339–374.MathSciNetzbMATHCrossRefGoogle Scholar
- [4]Osher, S.: “Numerical solution of singular perturbation problems and hyperbolic systems of conservation laws”, Math, studies no. 47 (1981), North Holland Publ. Comp., pp. 179–204.Google Scholar
- [5]Smoller, J.: “Shock waves and reaction diffusion equations”, Grund-lehren der Math, Wissenschaften, 258 Springer Verlag (1983).zbMATHCrossRefGoogle Scholar
- [6]Koppenol, P.J.: “Hyperbolic systems of conservation laws — theoretical and numerical aspects”, NLR Memorandum IW-84-009 U, (1984).Google Scholar
- [7]Rizzi, A., Viviand, H.: “Numerical methods for the computation of inviscid transonic flows with shock waves”, Notes on numerical Fluid Mechanics, Vol. 3, Vieweg (1979).Google Scholar
- [8]Radespiel, R., Kroll, N.: “Progress in the development of an efficient finite volume code for the three-dimensional Euler equations”, DFVLR, IB129–84/20, (1985).Google Scholar
- [9]Engquist, B., Majda, A.: “Absorbing boundary conditions for the numerical simulation of waves”, Math, of Comp., Vol. 31, No. 139 (1977), pp. 629–651.MathSciNetADSzbMATHCrossRefGoogle Scholar
- [10]Koppenol, P.J.: “3D Euler flow simulations on a CYBER 205 vector computer”, NLR TR 85054, (1985).Google Scholar