Abstract
This book concerns the development and application of numerical methods to the solution of the Euler equations. A brief sketch of the evolution of the ideas that led to the formulation of these equations, the problems to which they were applied, and the efforts to solve them before computers were available then sets the proper perspective for an appreciation of the material that follows.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Giacomelli, R.: The Aerodynamics of Leonardo da Vinci“. Aero J. Vol. 24, No. 240, 1930, pp. 121–134.
Tokaty, G.A.: “A History and Philosophy of Fluid Mechanics”. Foulis, London, 1971.
Bell, E.T.: “Men of Mathematics”. Simon and Schuster, New York, 1937.
Kline, M.: “Mathematical Thought from Ancient to Modern Times”. Oxford University Press, 1972.
Boyar, C.B.: “A History of Mathematics”. Wiley and Sons, New York, 1968.
Giacomelli, R., and Pistolesi, E.: “Historical Sketch”. In: Aerodynamic Theory, W.F. Durand (ed.), Vol. I, Springer, Berlin/ Heidelberg/New York, 1934.
von Kârmân, T.: “Aerodynamics”. Cornell Univ. Press, 1954.
Milne-Thomson, L.M.: “Theoretical Hydrodynamics”. 5th ed., Macmillan Co, New York, 1968.
Hunt, B.: “The Mathematical Basis and Numerical Principles of the Boundary Integral Method for Incompressible Potential Flow Over 3D Aerodynamic Configurations”. Numerical Methods in Fluid Dynamics, B. Hunt (ed.), Academic Press, New York, 1980, pp. 49–135.
Schlichting, H.: “Boundary Layer Theory”. 6th ed., McGraw-Hill, New York. 1968, pp. 178–184.
Southwell, R.V.: “Relaxation Methods in Theoretical Physics”. Oxford Univ. Press, 1946.
Courant, R., Friedrichs, K.O., Lewy, H.: “Uber die partiellen Differenzengleichungen der mathematischen Physik”. Math. Ann. 100, 1928, p. 32.
Fox, L. (ed): “Numerical Solution of Ordinary and Partial Differential Equations”. Pergamon Press, Oxford, 1962.
Rusanov, V.V.: “A Blunt Body in a Supersonic Stream”. Ann. Rev. Fluid Mech., Vol. 8, 1976, pp. 377–404.
Van Dyke, M.D.: “The Supersonic Blunt Body Problem — Review and Extension.” J. Aerospace Sci., Vol. 25, 1958, pp. 485–496.
Gilinskii, S.M., Telenin, G.F., Tinyakov, G.P.: “A Method for Computing Supersonic Flow Around Blunt Bodies”. Izv. Adad. Nauk, SSSR Rekh. Mash. 4, 1964, 9 (translated as NASA TT F297).
Dorodnitsyn, A.A.: “A Contribution to the solution of Mixed Problems of Transonic Aerodynamics”. Advances in Aeronautical Sciences, Vol. 2, Pergamon Press, New York, 1959.
Oswatitsch, K., Rues, D. (eds): “Transsonicum Symposium II”. Springer, Berlin, 1976.
Richtmyer, R.D., Morton, K.W.: “Difference Methods for Initial-Value Problems”. Interscience Publishers, New York, 1967.
Rusanov, V.V.: “The Calculation of the Interaction of Non-Stationary Shock Waves and Obstacles”. Zh. V.ch. Mat., Vol. 1, No. 2, 1961, pp. 267–279.
Rusanov, V.V.: “A Three-Dimensional Supersonic Gas Flow Past Smooth Blunt Bodies”. In Proc. 11th Int. Congress Appl. Mech, H. Görtler (ed.), Springer, Berlin, 1966.
Moretti, G., Abbett, M.: “A Time Dependent Computational Method for Blunt Body Flows”. AIAA J., Vol. 4, 1966, pp. 2136–2141.
Rizzi, A., Inouye, M.: “Time-Split Finite-Volume Method for Three-Dimensional Blunt-Body Flow”. AIAA Journal, Vol. 11, No. 11, Nov 1973, pp. 1478–1485.
Rizzi, A., Bailey, H.E.: “Finite Volume Solution of the Euler Equations for Steady Three-Dimensional Transonic Flow”. Proc. Fifth Internat. Conf. on Numer. Methods in Fluid Dynamics, A.I. van der Vooren and P.J. Zandbergen (eds.), Lecture Notes in Physics, 59, Springer, 1976, pp. 347–357.
Magnus, R., Yoshihara, H.: “Inviscid Transonic Flow Over Airfoils”, AIAA J. Vol. 8, No. 12, 1970, pp. 2157–2162.
Rizzi, A., Viviand, H. (eds.): “Numerical Methods for the Computation of Inviscid Transonic Flows with Shock Waves”. NNFM Vol. 3, Vieweg, Braunschweig/Wiesbaden, 1981.
Steinhoff, J.S., Reddy, K.C. (eds.): “Computational Fluid Dynamics in Aerospace Design”. UTSI Publication, Tullahoma, 1985.
Angrand, F., Dervieux, A., Desideri, J.A., Glowinski, R. (eds.): “Numerical Methods for the Euler Equations of Fluid Dynamics”. SIAM, Philadelphia, 1985.
Yoshihara, H., Sacher, P. (eds.): “Test Cases for Inviscid Flow Field Methods”. AGARD-AR-211, Paris, 1985.
Engqvist, B., Osher, S., Sommerville, R. (eds.): “Large Scale Computations in Fluid Mechnics”. Lectures in Applied Mathematics, Vol. 22, Ann Math. Soc., Providence, 1985.
Dervieux, A., Van Leer, B., Periaux, J., Rizzi, A. (eds.): “Numerical Simulation of Compressible Euler Flows”. NNFM Vol. 26, Vieweg, Braunschweig/Wiesbaden, 1989.
Elsenaar, A., Eriksson, L.-E. (eds.): “International Vortex Flow Experiment on Euler Code Validation”. FFA, Stockholm, 1987.
Zierep, J., Oertel, H. (eds.): “Symposium Transsonicum III”. Springer, Berlin 1989.
Bertin, J.J., Glowinski, R., Periaux, J. (eds.): “Hypersonics”. Birkhäuser, Boston, 1989.
Rizzi, A., Engqvist, B.: “Selected Topics in the Theory and Practice of Computational Fluid Dynamics–a Review”. J. Comp. Phys, Vol. 72, No. 1, Sept 1987, pp. 1–69.
Hirsch, C.: “Computational Methods for Inviscid and Viscous Flows”. John Wiley and Sons, Chichester, 1990.
Pandolfi, M.: “A Contribution to the Numerical Prediction of Unsteady Flows”. AIAA J., Vol. 22, No. 5, 1984, pp. 1217–1225.
Desideri, J.A., Dervieux, A.: “Compressible Flow Solvers Using Unstructured Grids”. VKI Lecture Series Notes 1988–05, Brussels, 1988.
Morgan, K., Pereire, J.: “Finite Element Methods for Compressible FLows”. VKI Lecture Series Notes 1987–08, Brussels, 1987.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer Fachmedien Wiesbaden
About this chapter
Cite this chapter
Eberle, A., Rizzi, A., Hirschel, E.H. (1992). Historical Origins of the Inviscid Model. In: Numerical Solutions of the Euler Equations for Steady Flow Problems. Notes on Numerical Fluid Mechanics (NNFM), vol 48. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-06831-0_1
Download citation
DOI: https://doi.org/10.1007/978-3-663-06831-0_1
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-528-07634-4
Online ISBN: 978-3-663-06831-0
eBook Packages: Springer Book Archive