Abstract
A combined algorithm using potential/Euler solvers, for transonic flow computations, is described. This combined scheme is substantially more efficient than the basic Euler solver. The potential equations are solved very effeciently by a Multigrid or an AF scheme. These solver require also considerably less computer memory than the corresponding Euler solver. The potential solver is used to provide initial approximation to the Euler solver, to determine the regions where the flow is vortical and where the Euler solver has to be used. Thus, the full Euler equations are solved only in some parts of the computational domain, and the potential equations are used elsewhere. Since the potential solver provides a relatively good approximation to the Euler solution, few (one or two) coupled iterative steps are adequate. The coupled scheme, is faster and requires less computer storage than current Euler solvers.
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References
Fuchs, L.: “Finite-difference methods for plane steady inviscid transonic flows” The Royal Institute of Technology Report. TRITA-GAD-2, ISSN 0281-7721 (1977).
Fuchs, L.: “Transonic flow computation by a multi-grid method”, GAMM-Workshop on Numerical Methods for the computation of Inviscid Transonic Flows with Shock Waves, Rizzi, A. and Viviand, H. (eds.) Vieweg & Sohn, 1979, pp. 58–65.
Jameson, A.: “A multi-grid scheme for transonic potential calculations on arbitrary grids”, Proc. 4-th AIAA CFD conference, pp. 122–146 (1979).
Hoist, T. L.: “Implicit algortihm for the conservative transonic full potential equation using an arbitrary mesh”, AIAA paper 78-1113 (1978).
Gu, C-Y., Fuchs, L.: “Numerical computation of transonic airfoil flows”, in Num. Meth. Laminar and Turbulent Flow-IV, Taylor, C., Olson, M.D., Gresho, P.M., Habashi, W.G. (eds.), Pineridge Press, Swansea, 1985, pp. 1501–1512. (Details in: Gu, Y-C.: Transonic flow computations. TRITA-GAD-8, ISSN 0281-7721, 1985).
Schmidt, W., Jameson, A.: “Application of multiple-grid methods for transonic flow calculations”. in ‘Lecture Notes in Mathematics', Hackbusch, W. and Trottenberg, U. (eds.), Springer Verlag, Berlin, 1982, pp. 599–613.
William, J., Usab, Jr., Murman, E.M.: “Embedded mesh solutions of the Euler equations using a multiple-grid method”, in ‘Advances in computational transonics’ Habashi W.G. (ed.), Pineridge Press, Swansea 1985, pp. 447–472.
Mulder, W. A.: “Computation of the quasi-steady gas flow in a spiral galaxy by means of a multigrid method”, 2nd Copper-Mountain Multigrid Conference, 1985.
Klopfer, G. and Nixon, D.: “Non-isentropic potential formulation for transonic flows”, AIAA paper 83-375 (1983).
Hafez, M., Lovell, D.: “Entropy and vorticity corrections for transonic flows”, AIAA paper 83-1926 (1983).
Jameson, A., Schmidt, W., Turkel, E.: “Numerical solution of the Euler equations by finite volume methods using Runge-Kutta time marching schemes”, AIAA Paper 81-1259 (1981).
Rizzi, A. W.: “Damped Euler-equation method to compute transonic flow around wing-body combinations”, AIAA J. 10, (1982), pp. 1321–1328.
Jameson, A.: A multi-grid solution method for the Euler equations, Proc. ICFD conference, Morton K.W. and Bains, M.J. (eds.), Oxford University Press, 1986.
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© 1986 Springer-Verlag
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Fuchs, L. (1986). A combined numerical scheme for transonic flows. In: Zhuang, F.G., Zhu, Y.L. (eds) Tenth International Conference on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics, vol 264. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0041805
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DOI: https://doi.org/10.1007/BFb0041805
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