Summary
Today’s computational methods are built upon physical and numerical models. Thus it is important to have an appreciation of the reasoning and thought processes that established our current understanding of the mechanics of fluids, all put in place before the age of numerical solutions. A brief sketch is given of the evolution of the ideas that led to the formulation of the equations governing fluid flow, the problems to which the equations were applied, and the efforts to solve them before computers were available. After the historical origins of the fluid-flow models are in place, the last section traces the transition undergone during the 20th Century, starting with analytical means to solve the mathematical problems that successively evolved into numerical approaches to solving them, thus leading up to the present time of the computational era.
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References
Giacomelli, R.: The Aerodynamics of Leonardo da Vinci. Aero J. 24(240), 121–134 (1930)
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)
Boyar, C.B.: A History of Mathematics. Wiley & Sons, New York (1968)
Giacomelli, R., Pistolesi, E.: Historical Sketch. In: Durand, W.F. (ed.) Aerodynamic Theory, vol. I. Springer, Berlin (1934)
von Kármán, T.: Aerodynamics. Cornell Univ. Press (1954)
Prandtl, L.: Über Flüssigkeitsbewegungen bei sehr kleiner Reibung. Verhandlungen des III. Internationalen Mathemathischen Kongresses, pp. 484–491 (1904)
Hirschel, E.H., Prem, H., Madelung, G. (eds.): Aeronautical Research in Germany – from Lilienthal until Today. Springer, Berlin (2004)
Milne-Thomson, L.M.: Theoretical Hydrodynamics, 5th edn. 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. In: Hunt, B. (ed.) Numerical Methods in Fluid Dynamics, pp. 49–135. Academic Press, New York (1980)
Schlichting, H.: Boundary Layer Theory, 6th edn., pp. 178–184. McGraw-Hill, New York (1968)
Southwell, R.V.: Relaxation Methods in Theoretical Physics. Oxford University Press, Oxford (1946)
Courant, R., Friedrichs, K.O., Lewy, H.: Uber die partiellen Differenzengleichungen der mathematischen Physik. Math. Ann. 100, 32 (1928)
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. 8, 377–404 (1976)
Van Dyke, M.D.: The Supersonic Blunt Body Problem Review and Extension. J. Aerospace Sci. 25, 485–496 (1958)
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, 9 (translated as NASA TT F297) (1964)
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)
Rizzi, A., Viviand, H. (eds.): Numerical Methods for the Computation of Inviscid Transonic Flows with Shock Waves. NNFM, vol. 3. Braunschweig/Wiesbaden, Vieweg (1981)
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 NonStationary Shock Waves and Obstacles. Zh. Vych. Mat. 1(2), 267–279 (1961)
Rusanov, V.V.: A Three-Dimensional Supersonic Gas Flow Past Smooth Blunt Bodies. In: Gortler, H. (ed.) Proc. 11th Int. Congress App1. Mech. Springer, Berlin (1966)
Moretti, G., Abbett, M.: A Time Dependent Computational Method for Blunt Body Flows. AIAA J. 4, 2136–2141 (1966)
Rizzi, A., Inouye, M.: Time-Split Finite-Volume Method for Three-Dimensional Blunt-Body Flow. AIAA Journal 11(11), 1478–1485 (1973)
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Rizzi, A., Hirschel, E.H. (2009). General Developments of Numerical Fluid Mechanics Until the Middle of the 20th Century. In: Hirschel, E.H., Krause, E. (eds) 100 Volumes of ‘Notes on Numerical Fluid Mechanics’. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70805-6_6
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