Aeronautics, and in particular aerodynamics, has been one of the main technological drivers for the development of computational fluid dynamics (CFD). This paper presents a personal account of the main advances in the development of solvers and shape optimization techniques, which have contributed to make CFD an essential part of the design process of modern aircraft.
Issue Section:
Research Papers
References
1.
Hess
, J. L.
, and Smith
, A. M. O.
, 1962
, “Calculation of Non-Lifting Potential Flow About Arbitrary Three-Dimensional Bodies
,” Douglas Aircraft Report No. ES 40622.2.
Rubbert
, P. E.
, and Saaris
, G. R.
, 1968
, “A General Three-Dimensional Potential-Flow Method Applied to V/STOL Aerodynamics
,” SAE
Paper No. 680304.10.4271/6803043.
Woodward
, F.
, 1973
, “An Improved Method for the Aerodynamic Analysis of Wing-Body-Tail Configurations in Subsonic and Supersonic Flow. Part 1: Theory and Application
,” Report No. NASA-CR-2228.4.
Hess
, J. L.
, 1990
, “Panel Methods in Computational Fluid Dynamiics
,” Annu. Rev. Fluid Mech.
, 22
, pp. 255
–274
.10.1146/annurev.fl.22.010190.0013515.
Spalding
, D. B.
, and Patankar
, S. V.
, 1972
, “A Calculation Procedure for Heat, Mass and Momentum Transfer in Three-Dimensional Parabolic Flows
,” Int. J Heat Mass Transfer
, 15
, pp. 1787
–1806
.6.
Launder
, B. E.
, and Spalding
, D. B.
, 1972
, Mathematical Models of Turbulence
, Academic Press
, New York
.7.
Murman
, E. M.
, and Cole
, J. D.
, 1971
, “Calculation of Plane Steady Transonic Flows
,” AIAA J.
, 9
, pp. 114
–121
.10.2514/3.61318.
Murman
, E. M.
, 1974
, “Analysis of Embedded Shock Waves Calculated by Relaxation Methods
,” AIAA J.
, 12
, pp. 626
–633
.10.2514/3.493099.
Jameson
, A.
, 1974
, “Iterative Solution of Transonic Flows Over Airfoils and Wings, Including Flows at Mach 1
,” Commun. Pure Appl. Math.
, 27
, pp. 283
–309
.10.1002/cpa.316027030210.
Jameson
, A.
, 1975
, “Transonic Potential Flow Calculations in Conservation Form
,” Proceedings of AIAA 2nd Computational Fluid Dynamics Conference
, Hartford
, pp. 148
–161
.11.
Eberle
, A.
, 1978
, “A Finite Volume Method for Calculating Transonic Potential Flow Around Wings From the Minimum Pressure Integral
,” Report No. NASA-TM-75324 [Messerschmitt-Bolkow-Blohm Internal Report No. MBB-UFE1407(0)].12.
Hafez
, M.
, South
, J. C.
, and Murman
, E. M.
, 1979
, “Artificial Compressibility Method for Numerical Solutions of the Transonic Full Potential Equation
,” AIAA J.
, 17
, pp. 838
–844
.10.2514/3.6123513.
Bauer
, F.
, Garabedian
, P.
, Korn
, D.
, and Jameson
, A.
, 1975
, Supercritical Wing Sections II
, Springer-Verlag
, New York
.14.
Caughey
, D. A.
, 1982
, “The Computation of Transonic Potential Flows
,” Annu. Rev. Fluid Mech.
, 14
, pp. 261
–283
.10.1146/annurev.fl.14.010182.00140115.
Melton
, J. E.
, Pandya
, S. A.
, and Steger
, J. L.
, 1993
, “3D Euler Flow Solutions Using Unstructured Cartesian and Prismatic Grids
,” Reno, NV, AIAA Paper No. 93-0331.16.
Samant
, S. S.
, Bussoletti
, J. E.
, Johnson
, F. T.
, Burkhart
, R. H.
, Everson
, B. L.
, Melvin
, R. G.
, Young
, D. P.
, Erickson
, L. L.
, and Madson
, M. D.
, 1987
, “TRANAIR: A Computer Code for Transonic Analyses of Arbitrary Configurations
,” AIAA Paper No. 87-0034.17.
Berger
, M.
, and LeVeque
, R. J.
, 1989
, “An Adaptive Cartesian Mesh Algorithm for the Euler Equations in Arbitrary Geometries
,” AIAA Paper No. 89-1930.18.
Landsberg
, A. M.
, Boris
, J. P.
, Sandberg
, W.
, and Young
, T. R.
, 1993
, “Naval Ship Superstructure Design: Complex Three-Dimensional Flows Using an Efficient, Parallel Method
,” High Performance Computing 1993: Grand Challenges in Computer Simulation
.19.
Baker
, T. J.
, 1986
, “Mesh Generation by a Sequence of Transformations
,” Appl. Num. Math.
, 2
, pp. 515
–528
.10.1016/0168-9274(86)90005-X20.
Eiseman
, P. R.
, 1979
, “A Multi-Surface Method of Coordinate Generation
,” J. Comput. Phys.
, 33
, pp. 118
–150
.10.1016/0021-9991(79)90031-721.
Eriksson
, L. E.
, 1982
, “Generation of Boundary-Conforming Grids Around Wing-Body Configurations Using Transfinite Interpolation
,” AIAA J.
, 20
, pp. 1313
–1320
.10.2514/3.798022.
Smith
, R. E.
, 1983
, “Three-Dimensional Algebraic Mesh Generation
,” Proceedings of AIAA 6th Computational Fluid Dynamics Conference
, Danvers, MA
, AIAA Paper No. 83-1904.23.
Thompson
, J. F.
, Thames
, F. C.
, and Mastin
, C. W.
, 1974
, “Automatic Numerical Generation of Body-Fitted Curvilinear Coordinate System for Field Containing Any Number of Arbitrary Two-Dimensional Bodies
,” J. Comput. Phys.
, 15
, pp. 299
–319
.10.1016/0021-9991(74)90114-424.
Thompson
, J. F.
, Warsi
, Z. U. A.
, and Mastin
, C. W.
, 1982
, “Boundary-Fitted Coordinate Systems for Numerical Solution of Partial Differential Equations: A Review
,” J. Comput. Phys.
, 47
, pp. 1
–108
.10.1016/0021-9991(82)90066-325.
Sorenson
, R. L.
, 1986
, “Elliptic Generation of Compressible Three-Dimensional Grids About Realistic Aircraft
,” International Conference on Numerical Grid Generation in Computational Fluid Dynamics
, J.
Hauser
and C.
Taylor
, eds., Landshut
, FRG
.26.
Sorenson
, R. L.
, 1988
, “Three-Dimensional Elliptic Grid Generation for an F-16,” Three-Dimensional Grid Generation for Complex Configurations: Recent Progress
, J. L.
Steger
and J. F.
Thompson
, eds., AGARDograph
.27.
Steger
, J. L.
, and Chaussee
, D. S.
, 1980
, “Generation of Body-Fitted Coordinates Using Hyperbolic Partial Differential Equations
,” SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput.
, 1
, pp. 431
–437
.10.1137/090103128.
Benek
, J. A.
, Buning
, P. G.
, and Steger
, J. L.
, 1985
, “A 3-D Chimera Grid Embedding Technique
,”AIAA 7th Computational Fluid Dynamics Conference
, Cincinnati, OH
, AIAA Paper No. 85-1523.29.
Benek
, J. A.
, Donegan
, T. L.
, and Suhs
, N. E.
, 1987
, “Extended Chimera Grid Embedding Scheme With Applications to Viscous Flows
,” AIAA 8th Computational Fluid Dynamics Conference
, Honolulu, HI
, AIAA Paper No. 87-1126.30.
Baker
, T. J.
, 1989
, “Automatic Mesh Generation for Complex Three-Dimensional Regions Using a Constrained Delaunay Triangulation
,” Eng. Comput.
, 5
, pp. 161
–175
.10.1007/BF0227421031.
May
, G.
, and Jameson
, A.
, 2005
, “Unstructured Algorithms for Inviscid and Viscous Flows Embedded in a Unified Solver Architecture: Flo3xx
,” AIAA 43rd Aerospace Sciences Meeting and Exhibit
, Reno, NV
, AIAA Paper No. 2005-0318.32.
Mavriplis
, D. J.
, 1997
, “Unstructured Grid Techniques
,” Annu. Rev. Fluid Mech.
, 29
(1
), pp. 473
–514
.10.1146/annurev.fluid.29.1.47333.
Artemov
, V.
, Beale
, S. B.
, de Vahl Davis
, G.
, Escudier
, M. P.
, Fueyo
, N.
, Launder
, B. E.
, Leonardi
, E.
, Malin
, M. R.
, Minkowycz
, W. J.
, Patankar
, S. V.
, Pollard
, A.
, Rodi
, W.
, Runchal
, A.
, and Vanka
, S. P.
, 2009
, “A Tribute to D.B. Spalding and His Contributions in Science and Engineering
,” Int. J. Heat Mass Transfer
, 52
(17–18
), pp. 3884
–3905
.10.1016/j.ijheatmasstransfer.2009.03.03834.
Paullay
, A. J.
, and MacCormack
, R. W.
, 1972
, “Computational Efficiency Achieved by Time Splitting of Finite Difference Operators
,” San Siego, CA
, AIAA Paper No. 72-154.35.
Bristeau
, M. O.
, Glowinski
, R.
, Periaux
, J.
, Perrier
, P.
, Pironneau
, O.
, and Poirier
, G.
, 1985
, “On the Numerical Solution of Nonlinear Problems in Fluid Dynamics by Least Squares and Finite Element Methods (II). Application to Transonic Flow Simulations
,” Comput. Methods Appl. Mech. Eng.
, 51
, pp. 363
–394
.10.1016/0045-7825(85)90039-836.
Lohner
, R.
, Morgan
, K.
, Peraire
, J.
, and Zienkiewicz
, O. C.
, 1985
, “Finite Element Methods for High Speed Flows
,” AIAA 7th Computational Fluid Dynamics Conference
, Cincinnati, OH
, AIAA Paper No. 85-1531.37.
Jameson
, A.
, Baker
, T. J.
, and Weatherill
, N. P.
, 1986
, “Calculation of Inviscid Transonic Flow Over a Complete Aircraft
,” AIAA 24th Aerospace Sciences Meeting
, Reno, NV
, AIAA Paper No. 86-010338.
Jameson
, A.
, and Baker
, T. J.
, 1987
, “Improvements to the Aircraft Euler Method
,” AIAA 25th Aerospace Sciences Meeting
, Reno, NV
, AIAA Paper No. 87-0452.39.
Stoufflet
, B.
, Periaux
, J.
, Fezoui
, F.
, and Dervieux
, A.
, 1987
, “Numerical Simulation of 3-D Hypersonic Euler Flows Around Space Vehicles Using Adapted Finite Elements
,” AIAA 25th Aerospace Sciences Meeting
, Reno, NV
, AIAA Paper No. 87-0560.40.
Batina
, J. T.
, 1990
, “Implicit Flux-Split Euler Schemes for Unsteady Aerodynamic Analysis Involving Unstructured Dynamic Meshes
,” AIAA Paper No. 90-0936.41.
Mavriplis
, D. J.
, and Jameson
, A.
, 1990
, “Multigrid Solution of the Navier–Stokes Equations on Triangular Meshes
,” AIAA J.
, 28
(8
), pp. 1415
–1425
.10.2514/3.2523342.
Mavriplis
, D. J.
, and Martinelli
, L.
, 1991
, “Multigrid Solution of Compressible Turbulent Flow on Unstructured Meshes Using a Two-Equation Model
,” AIAA 29th Aerospace Sciences Meeting
, Reno, NV, AIAA Paper No. 91-0237.43.
Barth
, T. J.
, 1994
, “Aspects of Unstructured Grids and Finite Volume Solvers for the Euler and Navier Stokes Equations
,” Lecture Series Notes 1994-05, von Karman Institute for Fluid Dynamics
, Brussels
.44.
Lax
, P. D.
, and Wendroff
, B.
, 1960
, “Systems of Conservation Laws
,” Commun. Pure. Appl. Math.
, 13
, pp. 217
–237
.10.1002/cpa.316013020545.
Godunov
, S. K.
, 1959
, “A Difference Method for the Numerical Calculation of Discontinuous Solutions of Hydrodynamic Equations
,” Mat. Sb.
, 47
, pp. 271
–306
[U.S. Department of Commerce, JPRS 7225 (1960)].46.
Stege
, J. L. R.
, and Warming
, R. F.
, 1981
, “Flux Vector Splitting of the Inviscid Gas Dynamic Equations With Applications to Finite Difference Methods
,” J. Comput. Phys.
, 40
, pp. 263
–293
.10.1016/0021-9991(81)90210-247.
Boris
, J. P.
, and Book
, D. L.
, 1973
, “Flux Corrected Transport. I. SHASTA, a Fluid Transport Algorithm That Works
,” J. Comput. Phys.
, 11
, pp. 38
–69
.10.1016/0021-9991(73)90147-248.
Van Leer
, B.
, 1974
, “Towards the Ultimate Conservative Difference Scheme. II. Monotonicity and Conservation Combined in a Second Order Scheme
,” J. Comput. Phys.
, 14
, pp. 361
–370
.10.1016/0021-9991(74)90019-949.
Van Leer
, B.
, 1982
, “Flux Vector Splitting for the Euler Equations
,” Proceedings of the 8th International Conference on Numerical Methods in Fluid Dynamics
, E.
Krause
, ed., Aachen
, pp. 507
–512
.50.
Roe
, P. L.
, 1981
, “Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes
,” J. Comput. Phys.
, 43
, pp. 357
–372
.10.1016/0021-9991(81)90128-551.
Osher
, S.
, and Solomon
, F.
, 1982
, “Upwind Difference Schemes for Hyperbolic Systems of Conservation Laws
,” Math. Comput.
, 38
, pp. 339
–374
.10.1090/S0025-5718-1982-0645656-052.
Harten
A.
, 1983
, “High Resolution Schemes for Hyperbolic Conservation Laws
,” J. Comput. Phys.
, 49
, pp. 357
–393
.10.1016/0021-9991(83)90136-553.
Osher
, S.
, and Chakravarthy
, S.
, 1984
, “High Resolution Schemes and the Entropy Condition
,” SIAM (Soc. Ind. Appl. Math.) J. Num Anal.
, 21
, pp. 955
–984
.10.1137/072106054.
Sweby
, P. K.
, 1984
, “High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws
,” J. Numer. Anal.
, 21
, pp. 995
–1011
.10.1137/072106255.
Anderson
, B. K.
, Thomas
, J. L.
, and Van Leer
, B.
, 1985
, “A Comparison of Flux Vector Splittings for the Euler Equations
,” AIAA 23rd Aerospace Sciences Meeting
, Reno, NV, AIAA Paper No. 85-0122.56.
Jameson
, A.
, 1985
, “Non-Oscillatory Shock Capturing Scheme Using Flux Limited Dissipation
,” Large Scale Computations in Fluid Mechanics, Part 1 (Lectures in Applied Mathematics, Vol. 22)
, B. E.
Engquist
, S.
Osher
, and R. C. J.
Sommerville
, eds., AMS
, Providence, RI
, pp. 345
–370
.57.
Yee
, H. C.
, 1985
, “On Symmetric and Upwind TVD Schemes
,” Proceedings of 6th GAMM Conference on Numerical Methods in Fluid Mechanics
, Gottingen
.58.
Hughes
, T. J. R.
, Franca
, L. P.
, and Mallet
, M.
, 1986
, “A New Finite Element Formulation for Computational Fluid Dynamics: I. Symmetric Forms of the Compressible Euler and Navier-Stokes Equations and the Second Law of Thermodynamics
,” Comput. Methods Appl. Mech. Eng.
, 59
, pp. 223
–234
.10.1016/0045-7825(86)90127-159.
Woodward
, P.
, and Colella
, P.
, 1984
, “The Numerical Simulation of Two-Dimensional Fluid Flow With Strong Shocks
,” J. Comput. Phys.
, 54
, pp. 115
–173
.10.1016/0021-9991(84)90142-660.
Barth
, T. J.
, and Jespersen
, D. C.
, 1989
, “The Design and Application of Upwind Schemes on Unstructured Meshes
,” AIAA 27th Aerospace Sciences Meeting
, Reno, NV, AIAA Paper No. 89-0366.61.
Barth
, T. J.
, and Frederickson
, P. O.
, 1990
, “Higher Order Solution of the Euler Equations on Unstructured Grids Using Quadratic Reconstruction
,” AIAA 28th Aerospace Sciences Meeting
, AIAA Paper No. 90-0013.62.
Jameson
, A.
, 1995
, “Analysis and Design of Numerical Schemes for Gas Dynamics, 1: Artificial Diffusion, Upwind Biasing, Limiters and Their Effect on Multigrid Convergence
,” Int. J. Comput. Fluid Dyn.
, 4
, pp. 171
–218
.10.1080/1061856950890452463.
Jameson
, A.
, 1995
, “Analysis and Design of Numerical Schemes for Gas Dynamics, 2: Artificial Diffusion and Discrete Shock Structure
,” Int. J. Comput. Fluid Dyn.
, 5
, pp. 1
–38
.10.1080/1061856950894073464.
Tatsumi
, S.
, Martinelli
, L.
, and Jameson
, A.
, 1995
, “A New High Resolution Scheme for Compressible Viscous Flows With Shocks
,” AIAA 33nd Aerospace Sciences Meeting
, Reno, NV, AIAA Paper No. 95-0466.65.
Liou
, M. S.
, 2001
, “Ten Years in the Making: AUSM-Family
,” Technical Memorandum No. NASA/TM-2001-210977.66.
Parthasarathy
, V.
, Kallinderis
, Y.
, and Nakajima
, K.
, 1995
, “A Hybrid Adaptation Method and Directional Viscous Multigrid With Prismatic-Tetrahedral Meshes
,” AIAA 33rd Aerospace Sciences Meeting, Reno, NV, AIAA Paper No. 95-0670.67.
Venkatakrishnan
, V.
, 1996
, “A Perspective on Unstructured Grid Flow Solvers
,” AIAA J.
, 34
, pp. 533
–547
.10.2514/3.1310168.
Venkatakrishnan
, V.
, 1988
, “Newton Solution of Inviscid and Viscous Problems
,” AIAA 26th Aerospace Sciences Meeting, Reno, NV, AIAA Paper No. 88-0413.69.
Giles
, M.
, Drela
, M.
, and Thompkins
, W. T.
, 1985
, “Newton Solution of Direct and Inverse Transonic Euler Equations
,” Proceedings AIAA 7th Computational Fluid Dynamics Conference
, Cininnati, OH
, AIAA Paper No. 85-1530, pp. 394
–402
.70.
Beam
, R. W.
, and Warming
, R. F.
, 1976
, “An Implicit Finite Difference Algorithm for Hyperbolic Systems in Conservation Form
,” J. Comput. Phys.
, 23
, pp. 87
–110
.10.1016/0021-9991(76)90110-871.
Pulliam
, T. H.
, and Steger
, J. L.
, 1980
, “Implicit Finite Difference Simulations of Three-Dimensional Compressible Flow
,” AIAA J.
, 18
, pp. 159
–167
.10.2514/3.5074572.
Hassan
, O.
, Morgan
, K.
, and Peraire
, J.
, 1989
, “An Adaptive Implicit/Explicit Finite-Element Method for High Speed Flows
,” AIAA 27th Aerospace Sciences Meeting
, Reno, NV, AIAA Paper No. 89-0363.73.
Lohner
, R.
, and Martin
, D.
, 1992
, “An Implicit Linelet-Based Solver for Incompressible Flows
,” AIAA 30th Aerospace Sciences Meeting
, Reno, NV, AIAA Paper No. 92-0668.74.
Jameson
, A.
, and Turkel
, E.
, 1981
, “Implicit Schemes and LU Decompositions
,” Math. Comput.
, 37
, pp. 385
–397
.10.2307/200743375.
Obayashi
, S.
, and Kuwakara
, K.
, 1984
, “LU Factorization of an Implicit Scheme for the Compressible Navier-Stokes Equations
,” AIAA 17th Fluid Dynamics and Plasma Dynamics Conference
, Snowmass, CO, AIAA Paper No. 84-1670.76.
Chakravarthy
, S. R.
, 1984
, “Relaxation Methods for Unfactored Implicit Upwind Schemes
,” AIAA 22nd Aerospace Sciences Meeting
, Reno, NV, AIAA Paper No. 84-0165.77.
Yoon
, S.
, and Jameson
, A.
, 1987
, “Lower-Upper Symmetric-Gauss-Seidel Method for the Euler and Navier-Stokes Equations
,” AIAA 25th Aerospace Sciences Meeting, Reno, NV, AIAA Paper No. 87-0600.78.
Chipman
, R.
, and Jameson
, A.
, 1979
, “Fully Conservative Numerical Solutions for Unsteady Irrotational Transonic Flow About Airfoils
,” AIAA 12th Fluid and Plasma Dynamics Conference
, Williamsburg, VA, AIAA Paper No. 79-1555.79.
Jameson
, A.
, Schmidt
, W.
, and Turkel
, E.
, 1981
, “Numerical Solution of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time Stepping Schemes
,” AIAA Paper No. 81-1259.80.
Jameson
, A.
, 1985
, “Multigrid Algorithms for Compressible Flow Calculations
,” 2nd European Conference on Multigrid Methods
, Cologne
, Princeton University
Report No. MAE 1743.81.
Jameson
, A.
, 1985
, “Transonic Flow Calculations for Aircraft
,” Numerical Methods in Fluid Dynamics (Lecture Notes in Mathematics)
, F.
Brezzi
, ed., Springer Verlag
, New York
, pp. 156
–242
.82.
Rizzi
, A.
, and Eriksson
, L. E.
, 1984
, “Computation of Flow Around Wings Based on the Euler Equations
,” J. Fluid Mech.
, 148
, pp. 45
–71
.10.1017/S002211208400224X83.
Fedorenko
, R. P.
, 1964
, “The Speed of Convergence of One Iterative Process
,” USSR Comput. Math. Math. Phys.
, 4
, pp. 227
–235
.10.1016/0041-5553(64)90253-884.
Brandt
, A.
, 1977
, “Multi-Level Adaptive Solutions to Boundary Value Problems
,” Math. Comput.
, 31
, pp. 333
–390
.10.1090/S0025-5718-1977-0431719-X85.
Hackbusch
, W.
, 1978
, “On the Multi-Grid Method Applied to Difference Equations
,” Computing
, 20
, pp. 291
–306
.10.1007/BF0225237886.
Ni
, R. H.
, 1982
, “A Multiple Grid Scheme for Solving the Euler Equations
,” AIAA J.
, 20
, pp. 1565
–1571
.10.2514/3.5122087.
Jameson
, A.
, 1983
, “Solution of the Euler Equations by a Multigrid Method
,” Appl. Math. Comput.
, 13
, pp. 327
–356
.10.1016/0096-3003(83)90019-X88.
Hall
, M. G.
, 1985
, “Cell Vertex Multigrid Schemes for Solution of the Euler Equations
,” Proceedings of IMA Conference on Numerical Methods for Fluid Dynamics
, Reading.89.
Jameson
, A.
, 1986
, “A Vertex Based Multigrid Algorithm for Three Dimensional Compressible Flow Calculations
,” ASME Symposium on Numerical Methods for Compressible Flow, Anaheim
.90.
Caughey
, D. A.
, 1987
, “A Diagonal Implicit Multigrid Algorithm for the Euler Equations
,” AIAA 25th Aerospace Sciences Meeting
, Reno, NV, AIAA Paper No. 87-453.91.
Anderson
, W. K.
, Thomas
, J. L.
, and Whitfield
, D. L.
, 1986
, “Multigrid Acceleration of the Flux Split Euler Equations
,” AIAA 24th Aerospace Sciences Meeting
, Reno, NV, AIAA Paper No. 86-0274.92.
Hemker
, P. W.
, and Spekreijse
, S. P.
, 1984
, “Multigrid Solution of the Steady Euler Equations
,” Proceedings of Oberwolfach Meeting on Multigrid Methods
.93.
Mulder
, W. A.
, 1989
, “A New Multigrid Approach to Convection Problems
,” J. Comput. Phys.
, 83
, pp. 303
–323
.10.1016/0021-9991(89)90121-694.
Mulder
, W. A.
, 1992
, “A High-Resolution Euler Solver Based on Multigrid, Semi-Coarsening, and Defect Correction
,” J. Comput. Phys.
, 100
, pp. 91
–104
.10.1016/0021-9991(92)90312-M95.
Allmaras
, S.
, 1993
, “Analysis of a Local Matrix Preconditioner for the 2-D Navier-Stokes Equations
,” AIAA 11th Computational Fluid Dynamics Conference
, Orlando, FL
, AIAA Paper No. 93-3330.96.
Allmaras
, S.
, 1995
, “Analysis of Semi-Implicit Preconditioners for Multigrid Solution of the 2-D Navier-Stokes Equations
,” AIAA 12th Computational Fluid Dynamics Conference
, San Diego, CA
, AIAA Paper No. 95-1651.97.
Allmaras
, S.
, 1997
, “Algebraic Smoothing Analysis of Multigrid Methods for the 2-D Compressible Navier-Stokes Equations
,” AIAA 13th Computational Fluid Dynamics Conference
, Snowmass, CO
, AIAA Paper No. 97-1954.98.
Pierce
, N. A.
, and Giles
, M. B.
, 1996
, “Preconditioning Compressible Flow Calculations on Stretched Meshes
,” AIAA 34th Aerospace Sciences Meeting
, Reno, NV, AIAA Paper No. 96-0889.99.
Pierce
, N. A.
, Giles
, M. B.
, Jameson
, A.
, and Martinelli
, L.
, 1997
, “Accelerating Three-Dimensional Navier-Stokes Calculations
,” AIAA 13th Computational Fluid Dynamics Conference
, Snowmass, CO
, AIAA Paper No. 97-1953.100.
Jameson
, A.
, and Mavriplis
, D. J.
, 1987
, “Multigrid Solution of the Euler Equations on Unstructured and Adaptive Grids
,” Multigrid Methods: Theory, Applications and Supercomputing (Lecture Notes in Pure and Applied Mathematics, Vol. 110)
, S.
McCormick
, ed., Springer, New York, pp. 413
–430
.101.
Peraire
, J.
, Peirö
, J.
, and Morgan
, K.
, 1992
, “A 3D Finite-Element Multigrid Solver for the Euler Equations
,” AIAA 30th Aerospace Sciences Conference
, Reno, NV
, AIAA Paper No. 92-0449.102.
Lallemand
, M. H.
, and Dervieux
, A.
, 1987
, “A Multigrid Finite-Element Method for Solving the Two-Dimensional Euler Equations
,” Proceedings of the 3rd Copper Mountain Conference on Multigrid Methods (Lecture Notes in Pure and Applied Mathematics)
, S. F.
McCormick
, ed., Copper Mountain
, pp. 337
–363
.103.
Lallemand
, M. H.
, Steve
, H.
, and Dervieux
, A.
, 1992
, “Unstructured Multigridding by Volume Agglomeration: Current Status
,” Comput. Fluids
, 21
, pp. 397
–433
.10.1016/0045-7930(92)90047-Y104.
Mavriplis
, D. J.
, and Venkatakrishnan
, V.
, 1996
, “A 3D Agglomeration Multigrid Solver for the Reynolds-Averaged Navier-Stokes Equations on Unstructured Meshes
,” Int. J. Numer. Methods Fluids
, 23
, pp. 1
–18
.10.1002/(SICI)1097-0363(19960930)23:6<527::AID-FLD429>3.0.CO;2-Z105.
Crumpton
, P. I.
, and Giles
, M. B.
, 1995
, “Implicit Time Accurate Solutions on Unstructured Dynamic Grids
,” AIAA 12th Computational Fluid Dynamics Conference
, San Diego, CA
, AIAA Paper No. 95-1671.106.
Jameson
, A.
, 1991
, “Time Dependent Calculations Using Multigrid, With Applications to Unsteady Flows Past Airfoils and Wings
,” AIAA 10th Computational Fluid Dynamics Conference
, Honolulu, HI
, AIAA Paper No. 91-1596.107.
Alonso
, J. J.
, and Jameson
, A.
, 1994
, “Fully-Implicit Time-Marching Aeroelastic Solutions
,” AIAA 32nd Aerospace Sciences Meeting
, Reno, NV, AIAA Paper No. 94-0056.108.
Alonso
, J. J.
, Martinelli
, L.
, and Jameson
, A.
, 1995
, “Multigrid Unsteady Navier-Stokes Calculations With Aeroelastic Applications
,” AIAA 33rd Aerospace Sciences Meeting and Exhibit
, Reno, NV, AIAA Paper No. 95-0048.109.
Belov
, A.
, Martinelli
, L.
, and Jameson
, A.
, 1995
, “A New Implicit Algorithm With Multigrid for Unsteady Incompressible Flow Calculations
,” AIAA 33rd Aerospace Sciences Meeting
, Reno, NV, AIAA Paper No. 95-0049.110.
Venkatakrishnan
, V.
, and Mavriplis
, D. J.
, 1996
, “Implicit Method for the Computation of Unsteady Flows on Unstructured Grids
,” J. Comput. Phys.
, 127
, pp. 380
–397
.10.1006/jcph.1996.0182111.
Hicks
, R. M.
, Murman
, E. M.
, and Vanderplaats
, G. N.
, 1974
, “An Assessment of Airfoil Design by Numerical Optimization
,” Ames Research Center, Moffett Field
, California, Report No. NASA-TM-X-3092.112.
Hicks
, R. M.
, and Henne
, P. A.
, 1978
, “Wing Design by Numerical Optimization
,” J. Aircr.
, 15
, pp. 407
–412
.10.2514/3.58379113.
Lions
, J. L.
, 1971
, Optimal Control of Systems Governed by Partial Differential Equations
, Springer-Verlag
, New York
[S. K. Mitter (translator)].114.
Jameson
, A.
, 1988
, “Aerodynamic Design via Control Theory
,” J. Sci. Comput.
, 3
, pp. 233
–260
.10.1007/BF01061285115.
Pironneau
, O.
, 1984
, Optimal Shape Design for Elliptic Systems
, Springer-Verlag
, New York
.116.
Jameson
, A.
, 1995
, “Optimum Aerodynamic Design Using CFD and Control Theory
,” AIAA 12th Computational Fluid Dynamics Conference
, San Diego, CA
, AIAA Paper No. 95-1729.117.
Jameson
, A.
, and Alonso
, J.J.
, 1996
, “Automatic Aerodynamic Optimization on Distributed Memory Architectures
,” 34th Aerospace Sciences Meeting and Exhibit
, Reno, NV, AIAA Paper No. 96-0409.118.
Jameson
, A.
, 1997
, “Re-Engineering the Design Process Through Computation
,” 35th Aerospace Sciences Meeting and Exhibit
, Reno, NV, AIAA Paper No. 97-0641.119.
Jameson
, A.
, Pierce
, N. A.
, and Martinelli
, L.
, 1997
, “Optimum Aerodynamic Design Using the Navier-Stokes Equations
,” 35th Aerospace Sciences Meeting and Exhibit
, Reno, NV, AIAA Paper No. 97-0101.120.
Jameson
, A.
, Martinelli
, L.
, and Pierce
, N.A.
, 1998
, “Optimum Aerodynamic Design Using the Navier-Stokes Equations
,” Theor. Comput. Fluid Dynamics
, 10
, pp. 213
–237
.10.1007/s001620050060121.
Jameson
, A.
, 1990
, “Automatic Design of Transonic Airfoils to Reduce the Shock Induced Pressure Drag
,” Proceedings of the 31st Israel Annual Conference on Aviation and Aeronautics
, Tel Aviv, pp. 5–17.122.
Jameson
, A.
, 1994
, “Optimum Aerodynamic Design via Boundary Control
,” AGARD-VKI Lecture Series, Optimum Design Methods in Aerodynamics, von Karman Institute for Fluid Dynamics
.123.
Reuther
, J.
, Jameson
, A.
, Alonso
, J. J.
, Rimlinger
, M. J.
, and Saunders
, D.
, 1997
, “Constrained Multipoint Aerodynamic Shape Optimization Using an Adjoint Formulation and Parallel Computers
,” 35th Aerospace Sciences Meeting and Exhibit
, Reno, NV, AIAA Paper No. 97-0103.124.
Reuther
, J.
, Alonso
, J. J.
, Vassberg
, J. C.
, Jameson
, A.
, and Martinelli
, L.
, 1997
, “An Efficient Multiblock Method for Aerodynamic Analysis and Design on Distributed Memory Systems
,” AIAA Paper No. 97-1893.125.
Baysal
, O.
, and Eleshaky
, M. E.
, 1992
, “Aerodynamic Design Optimization Using Sensitivity Analysis and Computational Fluid Dynamics
,” AIAA J.
, 30
(3
), pp. 718
–725
.10.2514/3.10977126.
Huan
, J. C.
, and Modi
, V.
, 1994
, “Optimum Design for Drag Minimizing Bodies in Incompressible Flow
,” Inverse Probl. Eng.
, 1
, pp. 1
–25
.10.1080/174159794088027570127.
Desai
, M.
, and Ito
, K.
, 1994
, “Optimal Controls of Navier-Stokes Equations
,” SIAM J. Control Optim.
, 32
(5
), pp. 1428
–1446
.10.1137/S0363012992224972128.
Anderson
, W. K.
, and Venkatakrishnan
, V.
, 1997
, “Aerodynamic Design Optimization on Unstructured Grids With a Continuous Adjoint Formulation
,” 35th Aerospace Sciences Meeting and Exhibit
, Reno, NV, AIAA Paper No. 97-0643.129.
Elliott
, J.
, and Peraire
, J.
, 1997
, “3-D Aerodynamic Optimization on Unstructured Meshes With Viscous Effects
,” AIAA Paper No. 97-1849.130.
Ta'asan
, S.
, Kuruvila
, G.
, and Salas
, M. D.
, 1992
, “Aerodynamic Design and Optimization in One Shot
,” 30th Aerospace Sciences Meeting and Exhibit
, Reno, NV, AIAA Paper No. 92-0025.131.
Shankaran
, S.
, Jameson
, A.
, and Martinelli
, L.
, 2008
, “Continuous Adjoint Method for Unstructured Grids
,” AIAA J.
, 46
, pp. 226
–239
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