[1]. John D. Anderson, Jr., A History of Aerodynamics, (Cambridge: Cambridge University Press, 1997), pp. 23, 25, 31, 35; Edme Mariotte, Traite de la percussion ou choc des corps (Paris: Academy of Sciences, 1673).
[2]. For further references in the history of fluid dynamics, see R. Giacomelli and E. Pistolesi, “Historical Sketch,” in William F. Durand, ed., Aerodynamic Theory, vol. 1 (Berlin: Julius Springer Verlag, 1934); Theodore von Kármán, Aerodynamics (Cornell: Cornell University Press, 1954); G.A. Tokaty, A History and Philosophy of Fluid Mechanics (Henley, UK: G.T. Foulis and Co., Ltd., 1971); Olivier Darrigol, Worlds of Flow: A History of Hydrodynamics from the Bernoullis to Prandtl (Oxford: Oxford University Press, 2005); and Michael Eckert, The Dawn of Fluid Dynamics: A Discipline Between Science and Technology (Weinheim, Germany: Wiley-VCH Verlag GmbH & Co. KGaA, 2006). All trace the evolution of fluid mechanics and aerodynamics in great detail, with excellent references to primary sources and other works.
[3]. Isaac Newton, Mathematical Principles of Natural Philosophy (Chicago: Encyclopedia Britannica, Inc., 1952 ed. of a 1687 work), pp. 159–267.
[4]. As explicated by Leonhard Euler in his Principles of the Motion of Fluids (1752), General Principles of the State of Equilibrium of Fluids (1753), and General Principles of the Motion of Fluids (1755).
[5]. Anderson, History of Aerodynamics, p. 89.
[6]. C.L.M.H. Navier, “Mémoire sur les du mouvement des fluids,” Mémoires de l’Academie Royale des Sciences, No. 6 (1823), pp. 389–416.
[7]. G.G. Stokes, “On the Theories of the Internal Friction of Fluids in Motion, and of the Equilibrium and Motion of Elastic Solids,” Transactions of the Cambridge Philosophical Society, vol. 8, No. 22 (1845), pp. 287–342.
[8]. This discussion is elaborated upon in the author’s Computational Fluid Dynamics: The Basics With Applications (New York: McGraw-Hill, 1995).
[9]. Ibid., p. 3.
[10]. L.F. Richardson, “The Approximate Arithmetical Solution by Finite Differences of Physical Problems Involving Differential Equations, With Application to the Stresses in a Masonry Dam,” Philosophical Transactions of the Royal Society of London, ser. A, vol. 210 (1910), pp. 307–357.
[11]. Many partial differential equations fall within one of the following categories: elliptic equations, parabolic equations, and hyperbolic equations, differentiated by their mathematical (and graphical) behavior. The setting-up of a given numerical solution of these equations depends critically on whether the equation in question is elliptic, parabolic, or hyperbolic.
[12]. Richard Courant, K.O. Friedrichs, and Hans Lewy, “Über die Partiellen Differenzengleichungen der Mathematischen Physik,” Mathematische Annalen, vol. 100, (1928), pp. 32–74. All three emigrated to the U.S.
[13]. Paul E. Ceruzzi, Beyond the Limits: Flight Enters the Computer Age (Cambridge: MIT Press, 1989), p. 15.
[14]. “Super Supercomputers,” Aviation Week (Feb. 16, 2009).
[15]. J.W. Strutt (Lord Rayleigh), “On the Resistance of Fluids,” Philosophical Magazine, ser. 57 (1876), pp. 430–441.
[16]. Milton O. Van Dyke, “Supersonic Flow Past a Family of Blunt Axisymmetric Bodies,” NASA Technical Report R-1 (1959).
[17]. In the old days of obtaining the computer results printed out on paper, I would tell my students to tear off the last page, keep it, and throw the rest out, because the last page contained the answer.
[18]. G. Moretti and M. Abbett, “A Time-Dependent Computational Method for Blunt Body Flows,” AIAA Journal, vol. 4, No. 12 (1966), pp. 2136–2141.
[19]. Earll Murman and Julian D. Cole, “Calculation of Plane Steady Transonic flows,” AIAA Journal, vol. 9, No. 1, (Jan. 1971), pp 114–121.
[20]. A. Jameson, W. Schmidt, and E. Turkel, “Numerical Solution of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes,” AIAA Paper 81-1259 (1981); see also A. Jameson, “Successes and Challenges in Computation Aerodynamics,” AIAA Paper 87-1184 (1987).
[21]. Eli Turkel, “Algorithms for the Euler and Navier-Stokes equations for supercomputers,” NASA CR-172543 (1985), p. 1.
[22]. R.W. MacCormack, “The Effect of Viscosity in Hypervelocity Impact Cratering,” AIAA Paper 69-354 (1969).
[23]. K.J. Weilmuenster, “High Angle of Attack Inviscid Flow Calculations of Shuttle-Like Vehicles with Comparisons to Flight Data,” AIAA Paper No. 83-1798 (1983). For Weilmuenster’s earlier work, see his “Solution of a large hydrodynamic problem using the STAR-100 computer,” NASA TM-X-7394 (1976).
[24]. J.S. Shang and S.J. Scherr, “Navier-Stokes Solution for a Complete Re-entry Configuration,” Journal of Aircraft, vol. 23, No. 12 (1986), pp. 881–888.
[25]. See P. Perrier, “Industrial Methodologies for the Design of Hypersonic Vehicles,” and Richard D. Neumann, “Defining the Aerothermodynamic Methodology,” in J.J. Bertin, et al., Hypersonics, vol. 1: Defining the Hypersonic Environment (Boston: Birkhäuser Boston, Inc., 1989), pp. 93–160.
[26]. The author has had the privilege of looking over Peter Gnoffo’s shoulder for two decades as he progressively developed LAURA. Some examples of work carried out with the LAURA code are given in Robert B. Greendyke and Peter A. Gnoffo “Convective and Radiative Heating for Vehicle Return from the Moon and Mars,” NASA TM-110185 (1995); Kenneth Sutton and Peter A. Gnoffo, “Multi-Component Diffusion with Application to Computational Aerothermodynamics,” AIAA Paper 98-2575 (1998); William L. Kleb, et al., “Collaborative Software Development in Support of Fast Adaptive AeroSpace Tools (FAAST),” AIAA Paper 2003-3978 (2003); Peter A. Gnoffo and Jeffrey A. White, “Computational Aerothermodynamic Simulation Issues on Unstructured Grids,” AIAA Paper 2004-2371 (2004); Peter A. Gnoffo, “Simulation of Stagnation Region Heating in Hypersonic Flow on Tetrahedral Grids,” AIAA Paper 2007-3960 (2007); Karen L. Bibb, et al., “Parallel, Gradient-Based Anisotropic Mesh Adaption for Re-Entry Vehicle Configurations,” AIAA Paper 2006-3579 (2007); Christopher O. Johnson, et al.,“The Influence on Radiative Heating for Earth Entry,” NASA Document ID 20080023455 (2008); Richard A. Thompson and Peter A. Gnoffo, “Implementation of a Blowing Boundary Condition in the LAURA Code,” NASA Document ID 20080008560 (2008); Peter A. Gnoffo, “Multi-Dimensional, Inviscid Flux Reconstruction for Simulation of Hypersonic Heating on Tetrahedral Grids,” AIAA Paper 2009-0599 (2009); and Gnoffo, Peter A., et al., “Implementation of Radiation, Ablation, and Free Energy Minimization Modules for Coupled Simulations of Hypersonic Flow,” AIAA Paper 2009-1399 (2009).
[27]. Judy Conlon, “OVERFLOW Code Empowers Computational Fluid Dynamics,” NASA Insights, vol. 5 (Apr. 1998).
[28]. For more on CFL3D and its applications, see J.L. Thomas, and R.W. Walters, “Upwind Relaxation Algorithms for the Navier-Stokes Equations,” AIAA Paper 85-1501-CP (1985); J.L. Thomas, B. van Leer, and R. W. Walters, “Implicit Flux-Split Schemes for the Euler Equations,” AIAA Paper 85-1680 (1985); W. K. Anderson, J. L. Thomas, and B. van Leer, “Comparison of Finite Volume Flux Vector Splitting for the Euler Equations,” AIAA Journal, vol. 24, No. 9, (Sept. 1986), pp. 1453–1460; J.L. Thomas, et al., “High-Speed Inlet Flows,” Symposium on Advances and Applications in CFD, Winter Annual Meeting of ASME, Chicago, IL, Nov. 1988; W.B. Compton, III, J.L. Thomas, W.K. Abeyounis, and M.L. Mason, “Transonic Navier-Stokes Solutions of Three-Dimensional Afterbody Flows,” NASA TM-4111 (1989); J.L. Thomas, “An Implicit Multigrid Scheme for Hypersonic Strong-Interaction Flowfields,” Comm. Applied Numerical Methods, vol. 8, (1992), pp. 683–693; and J.L. Thomas, “Reynolds Number Effects on Supersonic Asymmetrical Flows over a Cone,” Journal of Aircraft, vol. 30, No. 4, (Apr. 1993), pp. 488–495.