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Computational fluid dynamics, usually abbreviated as CFD, is a branch of fluid mechanics that uses numerical analysis and algorithms to solve and analyze problems that involve fluid flows. Computers are used to perform the calculations required to simulate the interaction of liquids and gases with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved. Ongoing research yields software that improves the accuracy and speed of complex simulation scenarios such as transonic or turbulent flows. Initial experimental validation of such software is performed using a wind tunnel with the final validation coming in full-scale testing, e.g. flight tests. ==Background and history== The fundamental basis of almost all CFD problems are the Navier–Stokes equations, which define any single-phase (gas or liquid, but not both) fluid flow. These equations can be simplified by removing terms describing viscous actions to yield the Euler equations. Further simplification, by removing terms describing vorticity yields the full potential equations. Finally, for small perturbations in subsonic and supersonic flows (not transonic or hypersonic) these equations can be linearized to yield the linearized potential equations. Historically, methods were first developed to solve the linearized potential equations. Two-dimensional (2D) methods, using conformal transformations of the flow about a cylinder to the flow about an airfoil were developed in the 1930s. One of the earliest type of calculations resembling modern CFD are those by Lewis Fry Richardson, in the sense that these calculations used finite differences and divided the physical space in cells. Although they failed dramatically, these calculations, together with Richardson's book "Weather prediction by numerical process", set the basis for modern CFD and numerical meteorology. In fact, early CFD calculations during the 1940s using ENIAC used methods close to those in Richardson's 1922 book. The computer power available paced development of three-dimensional methods. Probably the first work using computers to model fluid flow, as governed by the Navier-Stokes equations, was performed at Los Alamos National Lab, in the T3 group.〔(【引用サイトリンク】url=https://www.lanl.gov/orgs/t/t3/history.shtml#early )〕 This group was led by Francis H. Harlow, who is widely considered as one of the pioneers of CFD. From 1957 to late 1960s, this group developed a variety of numerical methods to simulate transient two-dimensional fluid flows, such as Particle-in-cell method (Harlow, 1957), Fluid-in-cell method (Gentry, Martin and Daly, 1966), Vorticity stream function method (Jake Fromm, 1963), and Marker-and-cell method (Harlow and Welch, 1965). Fromm's vorticity-stream-function method for 2D, transient, incompressible flow was the first treatment of strongly contorting incompressible flows in the world. The first paper with three-dimensional model was published by John Hess and A.M.O. Smith of Douglas Aircraft in 1967. This method discretized the surface of the geometry with panels, giving rise to this class of programs being called Panel Methods. Their method itself was simplified, in that it did not include lifting flows and hence was mainly applied to ship hulls and aircraft fuselages. The first lifting Panel Code (A230) was described in a paper written by Paul Rubbert and Gary Saaris of Boeing Aircraft in 1968.〔Rubbert, Paul and Saaris, Gary, "Review and Evaluation of a Three-Dimensional Lifting Potential Flow Analysis Method for Arbitrary Configurations," AIAA paper 72-188, presented at the AIAA 10th Aerospace Sciences Meeting, San Diego California, January 1972.〕 In time, more advanced three-dimensional Panel Codes were developed at Boeing (PANAIR, A502),〔Carmichael, R. and Erickson, L.L., "PAN AIR - A Higher Order Panel Method for Predicting Subsonic or Supersonic Linear Potential Flows About Arbitrary Configurations," AIAA paper 81-1255, presented at the AIAA 14th Fluid and Plasma Dynamics Conference, Palo Alto California, June 1981.〕 Lockheed (Quadpan),〔Youngren, H.H., Bouchard, E.E., Coopersmith, R.M. and Miranda, L.R., "Comparison of Panel Method Formulations and its Influence on the Development of QUADPAN, an Advanced Low Order Method," AIAA paper 83-1827, presented at the AIAA Applied Aerodynamics Conference, Danvers, Massachusetts, July 1983.〕 Douglas (HESS),〔Hess, J.L. and Friedman, D.M., "Analysis of Complex Inlet Configurations Using a Higher-Order Panel Method," AIAA paper 83-1828, presented at the AIAA Applied Aerodynamics Conference, Danvers, Massachusetts, July 1983.〕 McDonnell Aircraft (MACAERO),〔Bristow, D.R., "Development of Panel Methods for Subsonic Analysis and Design," NASA CR-3234, 1980.〕 NASA (PMARC)〔Ashby, Dale L.; Dudley, Michael R.; Iguchi, Steve K.; Browne, Lindsey and Katz, Joseph, “Potential Flow Theory and Operation Guide for the Panel Code PMARC”, NASA NASA-TM-102851 1991.〕 and Analytical Methods (WBAERO,〔Woodward, F.A., Dvorak, F.A. and Geller, E.W., "A Computer Program for Three-Dimensional Lifting Bodies in Subsonic Inviscid Flow," USAAMRDL Technical Report, TR 74-18, Ft. Eustis, Virginia, April 1974.〕 USAERO〔Katz, J. and Maskew, B., "Unsteady Low-Speed Aerodynamic Model for Complete Aircraft Configurations," AIAA paper 86-2180, presented at the AIAA Atmospheric Flight Mechanics Conference, Williamsburg Virginia, August 1986.〕 and VSAERO〔Maskew, Brian, "Prediction of Subsonic Aerodynamic Characteristics: A Case for Low-Order Panel Methods," AIAA paper 81-0252, presented at the AIAA 19th Aerospace Sciences Meeting, St. Louis, Missouri, January 1981.〕〔Maskew, Brian, “Program VSAERO Theory Document: A Computer Program for Calculating Nonlinear Aerodynamic Characteristics of Arbitrary Configurations”, NASA CR-4023, 1987.〕). Some (PANAIR, HESS and MACAERO) were higher order codes, using higher order distributions of surface singularities, while others (Quadpan, PMARC, USAERO and VSAERO) used single singularities on each surface panel. The advantage of the lower order codes was that they ran much faster on the computers of the time. Today, VSAERO has grown to be a multi-order code and is the most widely used program of this class. It has been used in the development of many submarines, surface ships, automobiles, helicopters, aircraft, and more recently wind turbines. Its sister code, USAERO is an unsteady panel method that has also been used for modeling such things as high speed trains and racing yachts. The NASA PMARC code from an early version of VSAERO and a derivative of PMARC, named CMARC,〔Pinella, David and Garrison, Peter, “Digital Wind Tunnel CMARC; Three-Dimensional Low-Order Panel Codes,” Aerologic, 2009.〕 is also commercially available. In the two-dimensional realm, a number of Panel Codes have been developed for airfoil analysis and design. The codes typically have a boundary layer analysis included, so that viscous effects can be modeled. Professor Richard Eppler of the University of Stuttgart developed the PROFILE code, partly with NASA funding, which became available in the early 1980s.〔Eppler, R.; Somers, D. M., "A Computer Program for the Design and Analysis of Low-Speed Airfoils," NASA TM-80210, 1980.〕 This was soon followed by MIT Professor Mark Drela's XFOIL code.〔Drela, Mark, "XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils," in Springer-Verlag Lecture Notes in Engineering, No. 54, 1989.〕 Both PROFILE and XFOIL incorporate two-dimensional panel codes, with coupled boundary layer codes for airfoil analysis work. PROFILE uses a conformal transformation method for inverse airfoil design, while XFOIL has both a conformal transformation and an inverse panel method for airfoil design. An intermediate step between Panel Codes and Full Potential codes were codes that used the Transonic Small Disturbance equations. In particular, the three-dimensional WIBCO code,〔Boppe, C.W., "Calculation of Transonic Wing Flows by Grid Embedding," AIAA paper 77-207, presented at the AIAA 15th Aerospace Sciences Meeting, Los Angeles California, January 1977.〕 developed by Charlie Boppe of Grumman Aircraft in the early 1980s has seen heavy use. Developers turned to Full Potential codes, as panel methods could not calculate the non-linear flow present at transonic speeds. The first description of a means of using the Full Potential equations was published by Earll Murman and Julian Cole of Boeing in 1970.〔Murman, Earll and Cole, Julian, "Calculation of Plane Steady Transonic Flow," AIAA paper 70-188, presented at the AIAA 8th Aerospace Sciences Meeting, New York New York, January 1970.〕 Frances Bauer, Paul Garabedian and David Korn of the Courant Institute at New York University (NYU) wrote a series of two-dimensional Full Potential airfoil codes that were widely used, the most important being named Program H.〔Bauer, F., Garabedian, P., and Korn, D. G., "A Theory of Supercritical Wing Sections, with Computer Programs and Examples," Lecture Notes in Economics and Mathematical Systems 66, Springer-Verlag, May 1972. ISBN 978-3540058076〕 A further growth of Program H was developed by Bob Melnik and his group at Grumman Aerospace as Grumfoil.〔Mead, H. R.; Melnik, R. E., "GRUMFOIL: A computer code for the viscous transonic flow over airfoils," NASA CR-3806, 1985.〕 Antony Jameson, originally at Grumman Aircraft and the Courant Institute of NYU, worked with David Caughey to develop the important three-dimensional Full Potential code FLO22〔Jameson A. and Caughey D., "A Finite Volume Method for Transonic Potential Flow Calculations," AIAA paper 77-635, presented at the Third AIAA Computational Fluid Dynamics Conference, Alburquerque New Mexico, June 1977.〕 in 1975. Many Full Potential codes emerged after this, culminating in Boeing's Tranair (A633) code,〔Samant, S.S., Bussoletti J.E., Johnson F.T., Burkhart, R.H., Everson, B.L., Melvin, R.G., Young, D.P., Erickson, L.L., Madson M.D. and Woo, A.C., "TRANAIR: A Computer Code for Transonic Analyses of Arbitrary Configurations," AIAA paper 87-0034, presented at the AIAA 25th Aerospace Sciences Meeting, Reno Nevada, January 1987.〕 which still sees heavy use. The next step was the Euler equations, which promised to provide more accurate solutions of transonic flows. The methodology used by Jameson in his three-dimensional FLO57 code〔Jameson, A., Schmidt, W. and Turkel, E., "Numerical Solution of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes," AIAA paper 81-1259, presented at the AIAA 14th Fluid and Plasma Dynamics Conference, Palo Alto California, 1981.〕 (1981) was used by others to produce such programs as Lockheed's TEAM program〔Raj, P. and Brennan, J.E., "Improvements to an Euler Aerodynamic Method for Transonic Flow Simulation," AIAA paper 87-0040, presented at the 25th Aerospace Sciences Meeting, Reno Nevada, January 1987.〕 and IAI/Analytical Methods' MGAERO program.〔Tidd, D.M., Strash, D.J., Epstein, B., Luntz, A., Nachshon A. and Rubin T., "Application of an Efficient 3-D Multigrid Euler Method (MGAERO) to Complete Aircraft Configurations," AIAA paper 91-3236, presented at the AIAA 9th Applied Aerodynamics Conference, Baltimore Maryland, September 1991.〕 MGAERO is unique in being a structured cartesian mesh code, while most other such codes use structured body-fitted grids (with the exception of NASA's highly successful CART3D code,〔Melton, J.E., Berger, M.J., Aftosmis, M.J. and Wong, M.D., "3D Application of a Cartesian Grid Euler Method," AIAA paper 95-0853, presented at the 33rd Aerospace Sciences Meeting and Exhibit, Reno Nevada, January 1995.〕 Lockheed's SPLITFLOW code〔Karmna, Steve L. Jr., "SPLITFLOW: A 3D Unstructurted Cartesian Prismatic Grid CFD Code for Complex Geometries," AIAA paper 95-0343, presented at the 33rd Aerospace Sciences Meeting and Exhibit, Reno Nevada, January 1995.〕 and Georgia Tech's NASCART-GT).〔Marshall, D., and Ruffin, S.M., " An Embedded Boundary Cartesian Grid Scheme for Viscous Flows using a New Viscous Wall Boundary Condition Treatment,” AIAA Paper 2004-0581, presented at the AIAA 42nd Aerospace Sciences Meeting, January 2004.〕 Antony Jameson also developed the three-dimensional AIRPLANE code〔Jameson, A., Baker, T.J. and Weatherill, N.P., "Calculation of Inviscid Tramonic Flow over a Complete Aircraft," AIAA paper 86-0103, presented at the AIAA 24th Aerospace Sciences Meeting, Reno Nevada, January 1986.〕 which made use of unstructured tetrahedral grids. In the two-dimensional realm, Mark Drela and Michael Giles, then graduate students at MIT, developed the ISES Euler program〔Giles, M., Drela, M. and Thompkins, W.T. Jr., "Newton Solution of Direct and Inverse Transonic Euler Equations," AIAA paper 85-1530, presented at the Third Symposium on Numerical and Physical Aspects of Aerodynamic Flows, Long Beach, California, January 1985.〕 (actually a suite of programs) for airfoil design and analysis. This code first became available in 1986 and has been further developed to design, analyze and optimize single or multi-element airfoils, as the MSES program.〔Drela, M. "Newton Solution of Coupled Viscous/Inviscid Multielement Airfoil Flows,", AIAA paper 90-1470, presented at the AIAA 21st Fluid Dynamics, Plasma Dynamics and Lasers Conference, Seattle Washington, June 1990.〕 MSES sees wide use throughout the world. A derivative of MSES, for the design and analysis of airfoils in a cascade, is MISES,〔Drela, M. and Youngren H., "A User's Guide to MISES 2.53", MIT Computational Sciences Laboratory, December 1998.〕 developed by Harold "Guppy" Youngren while he was a graduate student at MIT. The Navier–Stokes equations were the ultimate target of development. Two-dimensional codes, such as NASA Ames' ARC2D code first emerged. A number of three-dimensional codes were developed (ARC3D, OVERFLOW, CFL3D are three successful NASA contributions), leading to numerous commercial packages. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「computational fluid dynamics」の詳細全文を読む スポンサード リンク
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