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References
Theodorsen, Theodore, "Theory of Wing Sections of Arbitrary Shape", NACA TR 411, 1931.
Whitcomb, R. T., "A Study of the Zero Lift Drag-Rise Characteristics of Wing-Body Combinations Near the Speed of the Sound", NACA TR 1273, 1956.
Whitcomb, R. T., "Review of NASA Supercritical Airfoils", 9th ICAS Congress, Haifa, Paper 74-10, 1974.
Whitcomb, R. T., "A Design Approach and Selected Wind Tunnel Results at High Subsonic Speeds for Wing-Tip Mounted Winglets", NASA TN D8260, 1976.
Morawetz, C. S., "On the Non-Existence of Continuous Transonic Flows Past Profiles", Comm. Pure. Appl. Math., 9, 1956, pp. 45–48.
Chapman, D. R., "Computational Aerodynamics Development and Out-look", Dryden Lecture, 1979, AIAA Journal, 17, 1979, pp. 1293–1313.
Hess, J. L. and Smith, A. M. O., "Calculation of Non-Lifting Potential Flow About Arbitrary Three-Dimensional Bodies", Douglas Aircraft Report, ES 40622, 1962.
Rubbert, P. E. and Saaris, G. R., "A General Three Dimensional Potential Flow Method Applied to V/STOL Aerodynamics, SAE Paper 680304, 1968.
Hunt, B., "The Mathematical Basis and Numerical Principles of the Boundary Integral Method for Incompressible Potential Flow Over 3-D Aerodynamic Configurations", IMA Conference on Numerical Methods in Applied Fluid Dynamics, Reading, 1978, edited by B. Hunt, Academic Press, 1980, pp. 49–135.
Murman, E. M. and Cole, J. D., “Calculation of Plane Steady Transonic Flows, AIAA Journal, 9, 1971, pp. 114–121.
Jameson, Antony, "Iterative Solution of Transonic Flows Over Airfoils and Wings, Including Flows at Mach 1", Comm. Pure. Appl. Math., 27, 1974, pp. 283–309.
Albone, C. M., "A Finite Difference Scheme for Computing Supercritical Flows in Arbitrary Coordinate Systems", RAE Report 74090, 1974.
Murman, E. M., "Analysis of Embedded Shock Waves Calculated by Relaxation Methods", AIAA Journal, 12, 1974, pp. 626–633.
Jameson, Antony, "Transonic Potential Flow Calculations in Conservation Form", Proc AIAA 2nd Computational Fluid Dynamics Conference, Hartford, 1975, pp. 148–161.
Eberle, A., "A Finite Volume Method for Calculating Transonic Potential Flow Around Wings from the Minimum Pressure Integral", NASA TM 75324, translated from MBB UFE 1407(0), 1978.
Hafez, M., South, J.C. and Murman, E. M., "Artificial Compressibility Method for Numerical Solutions of Transonic Full Potential Equation", AIAA Journal, 17, 1979, pp. 838–844.
Holst, T. L. and Ballhaus, W. F., "Fast Conservative Schemes for the Full Potential Equation Applied to Transonic Flows", AIAA Journal, 17, 1979, pp. 145–152.
Lock, R. C., "A Modification to the Method of Garabedian and Korn", Proc. GAMM Workshop on Numerical Methods for the Computation of Inviscid Transonic Flows with Shock Waves", Stockholm, 1979, edited by A. Rizzi and H. Viviand, Vieweg, 1981, pp. 116–124.
Jameson, Antony, "Numerical Solution of the Nonlinear Partial Differential Equations of Mixed Type", Proc. SYNSPADE 1975, edited by B. Hubbard, Academic Press, pp. 275–320.
Engquist, B. and Osher, S., "Stable and Entropy Satisfying Approximations for Transonic Flow Calculations", Math. Comp., 34, 1980, pp. 45–75.
Goorjian, P., Meagher, M. and Van Buskirk, R., "Implicit Monotone Algorithms for the Small-Disturbance and Full Potential Equations Applied to Transonic Flows", AIAA Paper 83-0371, 1983.
Jameson, Antony and Caughey, D. A., "A Finite Volume Method for Transonic Flow Calculations", Proc. AIAA 3rd Computational Fluid Dynamics Conference, Albuquerque, 1977, pp. 35–54.
Jameson, Antony, "Remarks on the Calculation of Transonic Potential Flow by a Finite Volume Method", Proc. IMA Conference on Numerical Methods in Applied Fluid Dynamics, Reading, 1978, edited by B. Hunt, Academic Press, 1980, pp. 363–386.
Bristeau, M. O., Pironneau, O., Glowinski, R., Periaux, J., Perrier, P., and Poirier, G., "Application of Optimal Control and Finite Element Methods to the Calculation of Transonic Flows and Incompressible Viscous Flows", Proc. IMA Conference on Numerical Methods in Applied Fluid Dynamics, Reading, 1978, edited by B. Hunt, Academic Press, 1980, pp. 203–312.
Bristeau, M. O., Glowinski, R., Periaux, J., Perrier, P., Pironneau, O. and Poirier, G., "Transonic Flow Simulations by Finite Elements and Least Squares Methods", Proc. of 3rd International Conference on Finite Elements in Flow Problems, Banff, 1980, Vol. lm edited by D. H. Norrie, pp. 11–29.
Ballhaus, W. F., Jameson, A., and Albert, J., "Implicit Approximate Factorization Schemes for Steady Transonic Flow Problems", AIAA Journal, 16, 1978, pp. 573–579.
Holst, T. L., and Thomas, S. D., "Numerical Solution of Transonic Wing Flow Fields", AIAA Paper 82-0105, 1982.
Baker, T. J., "Approximate Factorization Methods", Proc. IMA Conference on Numerical Methods in Aeronautical Fluid Dynamics, Reading, 1981, edited by P. L. Roe, Academic Press, 1982, pp. 115–141.
Fedorenko, R. P., "The Speed of Convergence on One Iterative Process", USSR Comp. Math. and Math. Phys., 4, pp. 227–235.
South, J. C. and Brandt, A., "Application of A Multi-Level Grid Method to Transonic Flow Calculations", Proc. of Workshop on Transonic Flow Problems in Turbomachinery, Monterey, 1976, edited by T. C. Adamson and M. F. Platzer, Hemisphere, 1977, pp. 180–206.
Hackbush, W., "On the Multi-Grid Method Applied to Difference Equations", Computing, 20, 1978, pp. 291–306.
Jameson, Antony, "Acceleration of Transonic Potential Flow Calculations on Arbitrary Meshes by the Multiple Grid Method", Proc. AIAA 4th Computational Fluid Dynamics Conference, Williamsburg, 1979, pp. 122–146.
Caughey, D. A., "Multigrid Calculation of Three-Dimensional Transonic Potential Flows", AIAA Paper 83-0374, 1983.
Lax, P. D., "Weak Solutions of nonlinear Hyperbolic Equations and Their Numerical Computation", Comm. Pure Appl. Math., 7, 1954, pp. 159–193.
Lax, P. D. and Richtmyer, R. D., "Survey of the Stability of Linear Finite Difference Equations", Comm. Pure. Appl. Math., 9, 1956, pp. 267–293.
Lax, P. D. and Wendroff, B., "Systems of Conservation Laws", Comm. Pure Appl. Math., 13, 1960, pp. 217–237.
Lax, P. D. and Wendroff, B., "Difference Schemes for Hyperbolic Equations with Higher Order of Accuracy", Comm. Pure. Appl. Math., 17, 1964, pp. 381–398.
Richtmyer, R. D., and Morton, K. W., "Finite Difference Methods for Initial Value Problems", InterScience, 1967.
Kreiss, H. O., "Stability Theory of Difference Approximations for Mixed Initial Boundary Value Problems", I, Math. Comp., 22, 1968, pp. 703–714.
Gustaffson, B., Kreiss, H. O., and Sundstrom, A., "Stability Theory of Difference Approximations for Mixed Initial Boundary Value Problems", II, Math. Comp., 26, pp. 649–686.
Gustaffson, B., "The Convergence Rate for Diffeence Approximations to Mixed Initial Boundary Value Problems", Math. Comp., 29, 1975, pp. 396–406.
Gustaffson, B., and Oliger, J., "Stable Boundary Discretizations for a Class of Time Discretization of ut = ADo ux", Uppsala University Computer Science Report, 87, 1980.
Engquist, B., and Majda, A., "Absorbing Boundary Conditions for the Numerical Simulation of Waves", Math. Comp., 31, 1977, pp. 629–651.
Bayliss, A., and Turkel, E., "Far Field Boundary Conditions for Compressible Flows", Proc. Symposium on Numerical Boundary Condition Procedures, NASA CP 2201, 1981.
Moretti, Gino, "Calculations of Three Dimensional Inviscid Supersonic Flows", NASA CR 3573, 1982.
Arlinger, B. G., "Computation of Supersonic Flow Around Three Dimensional Wings", Proc. 13th, ICAS Congress, Seattle, 1982, Vol. 2, pp. 224–232.
Veuillot, J. P., and Viviand, H., "Methods Pseudo-Instationnaire pour le Calcul d'Ecoulement Transsoniques", ONERA Publication 1978-4, 1978.
Jameson, Antony, "Transonic Aerofoil Calculations Using the Euler Equations", Proc. IMA Conference on Numerical Methods in Aeronautic Fluid Dynamics, Reading, 1981, edited by P. L. Roe, Academic Press, 1982, pp. 289–308.
MacCormack, R. W., "The Effect of Viscosity in Hyper-Velocity Impact Cratering", AIAA Paper 69–354, 1969.
MacCormack, R. W. and Paullay, A. J., "Computational Efficiency Achieved by Time Splitting of Finite Difference Operators", AIAA Paper 72–154, 1972.
MacCormack, R. W. and Paullay, A. J., "The Influence of the Computational Mesh on Accuracy for Initial Value Problems with Discontinuous or Nonunique Solutions", Computers and Fluids, 2, 1974, pp. 339–360.
Rizzi, A. W. and Schmidt, W., "Finite Volume Method for Rotational Transonic Flow Problems", Proc. 2nd GAMM Conference on Numerical Methods in Fluid Mechanics, edited by E. H. Hirschel and W. Geller, GAMM, 1977, pp. 152–161.
Lerat, A. and Sidès, J., "A New Finite Volume Method for the Euler Equations with Applications to Transonic Flows", Proc. IMA Conference on Numerical Methods in Aeronautical Fluid Dynamics, Reading, 1981, edited by P. L. Roe, Academic Press, 1982, pp. 245–288.
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, 1981.
Schmidt, W., and Jameson, A., "Recent Developments in Finite Volume Time Dependent Techniques for Two and Three Dimensional Transonic Flows", Von Karman Institute Lecture Series 1982-04, 1982.
Jameson, Antony, and Baker, Timothy J., "Solution of the Euler Equations for Complex Configurations", Proc. AIAA 6th Computational Fluid Dynamics Conference, Danvers, 1983, pp. 293–302.
Courant, R., Isaacson, E., and Rees, M., "On the Solution of Nonlinear Hyperbolic Differential Equations", Comm. Pure. Appl. Math., 5, 1952, pp. 243–255.
Steger, J. L., and Warming, R. F., "Flux Vector Splitting of the Inviscid Gas Dynamics Equations with Applications to Finite Difference Methods", J. Comp. Phys., 40, 1981, pp. 263–293.
Lax, P. D., "Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves", SIAM Regional Series on Applied Mathematics, 11, 1973.
Jameson, Antony, and Lax, Peter D., "Conditions for the Construction of Multi-point Total Variation Diminishing Difference Schemes", Princeton University Report MAE 1650, 1984.
Osher, S., "Riemann Solvers, The Entropy Condition, and Difference Approximations", to appear in SIAM Journal on Numerical Analysis.
Harten, A., Hyman, J. M., Lax, P. D., and Keyfitz, B., "On Finite Difference Approximations and Entropy Conditions for Shocks", Comm. Pure Appl. Math., 29, 1976, pp. 297–322.
Harten, A., "High Resolution Schemes for Hyperbolic Conservation Laws", New York University Report DOE/ER 03077-175, 1982.
Roe, P. L., "Some Contributions to the Modelling of Discontinuous Flows", Proc. AMS/SIAM Summer Seminar on Large Scale Computation in Fluid Mechanics, San Diego, 1983.
Sweby, P. K., "High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws", to appear in J. Computational Physics.
Osher, Stanley and Chakravarthy, Sukumar, "High Resolution Schemes and the Entropy Condition", ICASE Report NASA CR 172218.
Boris, J. P., and Book, D. L., "Flux Corrected Transport, 1 SHASTA, A Fluid Transport Algorithm that Works", J. Computational Physics, 11, 1973, pp. 38–69.
Zalesak, S. "Fully Multidimensional Flux Corrected Transport Algorithm for Fluids", J. Computational Physics, 31, 1979, pp. 335–362.
van Leer, B., "Towards the Ultimate Conservative Difference Scheme. II Monotonicity and Conservation Combined in a Second Order Scheme", J. Computational Physics, 14, 1974, pp. 361–370.
Goodman, J. B. and Leveque, R. J., "On the Accuracy of Stable Schemes for 2-D Scalar Conservation Laws", to appear in Math. Comp.
van Leer, B., "Flux Vector Splitting for the Euler Equations", Proc. 8th International Conference on Numerical Methods in Fluid Dynamics Aachen, 1982, edited by E. Krause, Springer, 1982, pp. 507–512.
Godunov, S. K., "A Difference Method for the Numerical Calculation of Discontinuous Solutions of Hydrodynamic Equations", Mat. Sbornik, 47, 1959, pp. 271–306, translated as JPRS 7225 by U.S. Dept. of Commerce, 1960.
Roe, P. L., "The Use of the Riemann Problem in Finite Difference Schemes", Proc. 7th International Conference on Numerical Methods in Fluid Dynamics, Stanford 1980, edited by W. C. Reynolds and R. W. MacCormack, Springer, 1981, pp. 354–349.
Roe, P. L., "Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes", J. Computational Physics, 43, 1981, pp. 357–372.
Van der Houwen, "Construction of Integration Formulas for Initial Value Problems" North Holland, 1977.
Sonneveld, P., and van Leer, B., "Towards the Solution of Van der Houwen's Problems", to appear in Nieuw Archief voor Wiskunde.
Roe, P. L., and Pike, J., "Restructuring Jameson's Finite Volume Scheme for the Euler Equations", RAE Report, 1983.
Beam, R. W., and Warming, R. F., "An Implicit Finite Difference Algorithm for Hyperbolic System in Conservation Form", J. Comp. Phys., 23, 1976, pp. 87–110.
Rizzi, A., and Skollermo, G., "Semi-Direct Solution to Steady Transonic Flow by Newton's Method", Proc. 7th International Conference on Numerical Methods in Fluid Dynamics, Stanford, 1980, edited by W. C. Reynolds and R. W. MacCormack, Springer, 1981, pp. 349–353.
Gourlay, A. R., and Mitchell, A. R., "A Stable Implicit Difference Method for Hyperbolic Systems in Two Space Variables", Numer. Math., 8, 1966, pp. 367–375.
Briley, W. R. and MacDonald, H., "Solution of the Three Dimensional Compressible Navier-Stokes Equations by an Implicit Technique", Proc. 4th International Conference on Numerical Methods in Fluid Dynamics, 1974.
Pulliam, T. H., and Steger, J. L., "Implicit Finite Difference Simulations of Three-Dimensional Compressible Flow", AIAA Journal, 18, 1980, pp. 159–167.
Jameson, Antony, and Turkel, E., "Implicit Schemes and LU Decompositions", Math. Comp. 37, 1981, pp. 385–397.
Buratynski, E. K., "A Lower-Upper Factored Implicit Scheme for the Numerical Solution of the Euler Equations Applied to Arbitrary Cascades", Cornell University Thesis, 1983.
MacCormack, R. W., "A Numerical Method for Solving the Equations of Compressible Viscous Flows", AIAA Paper 81–110, 1981.
Lerat, A., Sidès, J., and Daru, V., "An Implicit Finite Volume Scheme for Solving the Euler Equations", Proc. 8th International Conference on Numerical Methods in Fluid Dynamics, Aachen, 1982, edited by E. Krause, Springer, 1982, pp. 343–349.
Ni, R. H., "A Multiple Grid Scheme for Solving the Euler Equations", Proc. AIAA 5th Computational Fluid Dynamics Conference, Palo Alto, 1981, pp. 257–264.
Jameson, Antony, "Solution of the Euler Equations by a Multigrid Method", Applied Mathematics and Computation, 13, 1983, pp. 327–356.
Bauer, F., Garabedian, P., Korn, D., and Jameson, A., "Supercritical Wing Sections II", Springer, 1975.
Lock, R. C. and Firmin, M. C. P., "Survey of Techniques for Estimating Viscous Effects in External Aerodynamics", Proc. IMA Conference on Numerical Methods in Aeronautical Fluid Dynamics, Reading, 1980, edited by P. L. Roe, Academic Press, 1982, pp. 337–430.
Le Balleur, J. C., "Numerical Viscid-Inviscid Interaction in Steady and Unsteady Flows", Proc. 2nd Symposium on Numerical and Physical Aspects of Aerodynamic Flows, Long Beach, 1983.
Melnik, R. E., "Turbulent Interactions on Airfoils at Transonic Speeds — Recent Developments", Proc. AGARD Conference on Computation of Viscous-Inviscid Interactions, Colorado Springs, 1980, AGARD CP 291, Paper No. 10.
Lighthill, M. J., "On Displacement Thickness", J. Fluid Mechanics, 4, 1958, pp. 383–392.
Johnston, W., and Sockol, P., "Matching Procedure for Viscous Inviscid Interactive Calculations", AIAA Journal, 17, pp. 661–663.
Carter, J. E., "A New Boundary Layer Inviscid Interaction Technique for Separated Flow", Proc. AIAA 4th Computational Fluid Dynamics Conference, Williamsburg, 1979, pp. 45–55.
Le Balleur, J. C., Peyret, R., and Viviand, H., "Numerical Studies in High Reynolds Number Aerodynamics", Computers and Fluids, 8, 1980, pp. 1–30.
Collyer, M. R., and Lock, R. C., "Prediction of Viscous Effects in Steady Transonic Flow Past an Aerofoil", Aeronautical Quarterly, 30, 1979, pp. 485–505.
Le Balleur, J. C., "Strong Matching Methods for Computing Transonic Viscous Flow Including Wakes and Separations — Lifting Airfoils", La Recherche Aerospatiale, 3, 1981.
Melnik, R. E., Chow, R. R., Mead, H. R., and Jameson, A., "A Multigrid Method for the Computation of Viscid/Inviscid Interactions on Airfoils", AIAA Paper 83-0234, 1983.
Whitfield, D. L., Thomas, J. L., Jameson, A., and Schmidt, W., "Computation of Transonic Viscous Inviscid Interacting Flow", Proc. 2nd Symposium on Numerical and Physical Aspects of Aerodynamic Flows, Long Beach, 1983.
Mehta, Unmeel, and Lomax, Harvard, "Reynolds Averaged Navier Stokes Computations of Transonic Flow — the State of the Art", Proc. Transonic Perspectives Symposium, Moffett Field, 1979, edited by D. Nixon, AIAA, 1981, pp. 297–375.
MacCormack, R. W., and Baldwin, B. S., "A Numerical Method for Solving the Navier Stokes Equations with Application to Shock Boundary Layer Interactions, AIAA Paper 75-1, 1975.
Deiwert, G. S., "Numerical Simulation on High Reynolds Number Transonic Flows," AIAA Journal, 134, 1975, pp. 1354–1359.
Shang, J. S., and Hankey, W. L., "Computation of Flow Past a Hypersonic Cruiser", Proc. 2nd Symposium on Numerical and Physical Aspects of Aerodynamic Flows, Long Beach, 1983.
Beam, R., and Warming, R. F., "An Implicit Factored Scheme for the Compressible Navier Stokes Equations", AIAA Journal, 16, 1978, pp. 393–402.
Bradshaw, P., "Structure of Turbulence in Complex Flows", AGARD LS 94, 1978.
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Jameson, A. (1985). Transonic flow calculations for aircraft. In: Brezzi, F. (eds) Numerical Methods in Fluid Dynamics. Lecture Notes in Mathematics, vol 1127. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074531
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