Skip to main content
SpringerLink
Log in
Book cover

Computational Techniques for Fluid Dynamics 2 pp 128–203Cite as

Inviscid Flow

  • Chapter

  • 1321 Accesses

Part of the book series: Scientific Computation ((SCIENTCOMP))

Abstract

In this chapter the basic computational techniques developed in Chaps. 3–10 will be extended to construct effective computational methods for inviscid flow. Sects. 11.3 and 11.6.1 provide an appropriate framework for this process. Computational techniques will be selected on the basis of those that are considered to be the most effective without regard for the need to achieve a comprehensive review. This often means that newer methods are described at the expense of older but less efficient methods.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   79.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Abbett, M.J. (1973): Proc. 1st AIAA Computational Fluid Dynamics Conf., AIAA, New York, pp. 153–172

    Google Scholar 

  • Anderson, W.K., Thomas, J.L., Whitfield, D.L. (1988): AIAA J. 26, 649–654

    Article  ADS  Google Scholar 

  • Ballhaus, W.F., Jameson, A., Albert, J. (1978): AIAA J. 16, 573–579

    Article  ADS  Google Scholar 

  • Bayliss, A., Turkel, E. (1982): J. Comput. Phys. 48, 182–199

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Book, D.L., Boris, J.P., Hain, K. (1975): J. Comput. Phys. 18, 248–283

    Article  MATH  ADS  Google Scholar 

  • Book, D.L. (ed.) (1981): Finite-Difference Techniques for Vectorized Fluid Dynamics Calculations, Springer Ser. Comput. Phys. (Springer, Berlin, Heidelberg)

    Google Scholar 

  • Boris, J.P., Book, D.L. (1973): J. Comput. Phys. 11, 38–69

    Article  MATH  ADS  Google Scholar 

  • Boris, J.P., Book, D.L. (1976): Methods Comput. Phys. 16, 85–129

    Google Scholar 

  • Brebbia, C.A. (1978): The Boundary Element Method for Engineers (Pentech Press, London)

    Google Scholar 

  • Carmichael, R.L., Erikson, L.L. (1981): “PAN AIR-A Higher Order Panel Method for Predicting Subsonic or Supersonic Linear Potential Flows about Arbitrary Configurations”, AIAA Paper 81-1255

    Google Scholar 

  • Catherall, D. (1982): AIAA J. 20, 1057–1063

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Caughey, D.A. (1982): Annu. Rev. Fluid Mech. 14, 261–283

    Article  MathSciNet  ADS  Google Scholar 

  • Chakravarthy, S.R. (1983): AIAA J. 21, 699–706

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Chakravarthy, S.R. (1986): “Algorithmic Trends in Computational Fluid Dynamics” in Proc. Int. Symp. Comp. Fluid Dynamics, ed. K. Oshima (Japan Soc. of Comp. Fluid Dynamics, Tokyo) Vol. 1, pp. 163–173

    Google Scholar 

  • Chakravarthy, S.R., Anderson, D.A., Salas, M.D. (1980): “The Split-Coefficient Matrix Method for Hyperbolic Systems of Gas Dynamic Equations”, AIAA Paper 80-0268

    Google Scholar 

  • Chakravarthy, S.R., Osher, S. (1983): “High Resolution Applications of the Osher Upwind Scheme for the Euler Equations”, AIAA Paper 83-1943

    Google Scholar 

  • Chakravarthy, S.R., Osher, S. (1985): Lect. Appl. Math. 22, 57–86

    MathSciNet  Google Scholar 

  • Chima, R.V., Johnson, G.M. (1985): AIAA J. 23, 23–32

    Article  MATH  ADS  Google Scholar 

  • Cole, J.D. (1975): SIAM J. Appl. Math. 29, 763–787

    Article  MathSciNet  MATH  Google Scholar 

  • Colella, P., Woodward, P.R. (1984): J. Comput. Phys. 54, 174–201

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Dadone, A., Magi, V. (1986): AIAA J. 24, 1277–1284

    Article  ADS  Google Scholar 

  • Dadone, A., Moretii, G. (1988): AIAA J. 26, 409–424

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Dadone, A., Napolitano, M. (1983): AIAA J. 21, 1391–1399

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Dadone, A., Napolitano, M. (1985): Comput. Fluids 13, 383–395

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Davis, R.L., Ni, R.H., Bowley, W.W. (1984): AIAA J. 22, 1573–1581

    Article  MATH  ADS  Google Scholar 

  • Deconinck, H., Hirsch, C.H. (1985): In Advances in Computational Transonics, ed. by W.G. Habashi (Pineridge Press, Swansea) pp. 733–775

    Google Scholar 

  • Ecer, A., Akay, H.U. (1985): In Advances in Computational Transonics, ed. by W.G. Habashi (Pineridge Press, Swansea) pp. 777–810

    Google Scholar 

  • Fletcher, C.A.J. (1975): AIAA J. 13, 1073–1078

    Article  ADS  Google Scholar 

  • Fletcher, C.A.J. (1984): Computational Galerkin Methods, Springer Ser. Comput. Phys. (Springer, Berlin, Heidelberg)

    Google Scholar 

  • Fletcher, C.A.J., Morton, K.W. (1986): “Oblique Shock Reflection by the Characteristic Galerkin Method”, in Proc. Ninth Australasian Fluid Mechanics Conference, ed. by P.S. Jackson (University of Auckland, Auckland), pp. 411–415

    Google Scholar 

  • Flores, J., Holst, T.L., Kwak, D., Batiste, D.M. (1983): “A New Consistent Spatial Differencing Scheme for the Transonic Full Potential Equation”, AIAA Paper 83-0373

    Google Scholar 

  • Flores, J., Barton, J., Holst, T., Pulliam, T. (1985): 9th Int. Conf. Numer. Methods Fluid Dynamics, ed. by Soubbaramayer, J.P. Boujot, Lecture Notes in Physics, Vol. 218 (Springer, Berlin, Heidelberg) pp. 213–218

    Google Scholar 

  • Goorjian, P. (1985): In Advances in Computational Transonics, ed. by W.G. Habashi (Pineridge Press, Swansea) pp. 215–255

    Google Scholar 

  • Habashi, W.G. (ed.) (1985): Advances in Computational Transonics (Pineridge Press, Swansea) pp. 23–58

    MATH  Google Scholar 

  • Hafez, M.M. (1985): In Advances in Computational Transonics, ed. by W.G. Habashi (Pineridge Press, Swansea) pp. 23–58

    Google Scholar 

  • Hall, M.G. (1984): R.A.E. Tech. Rep. 84013

    Google Scholar 

  • Harten, A. (1983): J. Comput. Phys. 49, 357–393

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Harten, A., Lax, P.D., van Leer, B. (1983): SIAM Rev. 25, 35–61

    Article  MathSciNet  MATH  Google Scholar 

  • Hemker, P.W. (1986): In 10th Int. Conf. Numer. Methods in Fluid Dynamics, ed. by F.G. Zhuang, Y.L. Zhu, Lecture Notes in Physics, Vol. 264 (Springer, Berlin, Heidelberg) pp. 308–313

    Google Scholar 

  • Hess, J.L. (1975): Comput. Methods Appl. Mech. Eng. 5, 145–196

    Article  MATH  ADS  Google Scholar 

  • Hess, J.L. (1990): Annu. Rev. Fluid Mech. 22, 255–274

    Article  ADS  Google Scholar 

  • Hess, J.L., Smith, A.M.O. (1967): Prog. Aeronaut. Sci. 8, 1–138

    Article  MATH  Google Scholar 

  • Holst, T. (1979): AIAA J. 17, 1038–1045

    Article  MATH  ADS  Google Scholar 

  • Holst, T. (1985): In Advances in Computational Transonics, ed. by W.G. Habashi (Pineridge Press, Swansea) pp. 59–82

    Google Scholar 

  • Holst, T., Ballhaus, W.F. (1979): AIAA J. 17, 145–152

    Article  MATH  ADS  Google Scholar 

  • Holt, M. (1984): Numerical Methods in Fluid Dynamics, 2nd ed., Springer Ser. Comput. Phys. (Springer, Berlin, Heidelberg)

    Google Scholar 

  • Hughes, T.J.R., Mallet, M. (1985): Finite Elements in Fluids 6, 339–353

    Google Scholar 

  • Hussaini, M.Y., Zang, T.A. (1987): Annu. Rev. Fluid Mech. 19, 339–367

    Article  ADS  Google Scholar 

  • Isaacson, E., Keller, H.B. (1966): Analysis of Numerical Methods (Wiley, New York)

    MATH  Google Scholar 

  • Jameson, A. (1978): “Transonic Flow Calculations”, in Computational Fluid Dynamics, ed. by H.J. Wirz, J.J. Solderen (Hemisphere, Washington, D.C.) pp. 1–87

    Google Scholar 

  • Jameson, A. (1979): “Acceleration of Transonic Potential Flow Calculations on Arbitrary Meshes by the Multiple Grid Method”, AIAA Paper 79-1458

    Google Scholar 

  • Jameson, A. (1983): Appl. Math. Comput. 13, 327–356

    Article  MathSciNet  MATH  Google Scholar 

  • Jameson, A., Baker, T. (1986): In 10th Int. Conf. Numer. Methods in Fluid Dynamics, ed. by F.G. Zhuang, Y.L. Zhu, Lecture Notes in Physics, Vol. 264 (Springer, Berlin, Heidelberg) pp. 334–344

    Google Scholar 

  • Jameson, A., Schmidt, W., Turkel, E. (1981): “Numerical Solution of the Euler Equations by Finite Volume Methods using Runge-Kutta Time Stepping Schemes”, AIAA Paper 81-1259

    Google Scholar 

  • Jaswon, M.A., Symm, G.T. (1977): Integral Equation Methods in Potential Theory and Elastostatics (Academic, London)

    MATH  Google Scholar 

  • Johnson, G.M. (1983): Appl. Math. Comput. 13, 357–380.

    Article  MathSciNet  ADS  Google Scholar 

  • Klopfer, G.H., Nixon, D. (1984): AIAA J. 22, 770–776

    Article  MATH  ADS  Google Scholar 

  • Kraus, W. (1978): “Panel Methods in Aerodynamics”, in Numerical Methods in Fluid Dynamics, ed. by H.J. Wirz, J.J. Smolderen (Hemisphere, Washington, D.C.) pp. 237–297

    Google Scholar 

  • Kuethe, A.M., Chow, C.Y. (1976): Foundations of Aerodynamics (Wiley, New York)

    Google Scholar 

  • Kutler, P., Lomax, H. (1971): J. Spacecr. & Rockets, 8, 1175–1182

    Article  ADS  Google Scholar 

  • Kutler, P., Warming, R.F., Lomax, H. (1973): AIAA J. 11, 196–204

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Lapidus, A. (1967): J. Comput. Phys. 2, 154–177

    Article  MATH  ADS  Google Scholar 

  • Lax, P., Wendroff, B. (1960): Commun. Pure Appl. Math. 13, 217–237

    Article  MathSciNet  MATH  Google Scholar 

  • Lerat, A., Peyret, R. (1975): Rech. Aerosp. 1975-2, 61–79

    MathSciNet  Google Scholar 

  • Lerat, A., Sides, J. (1982): Proc. Conf. Numerical Methods in Aeronautical Fluid Dynamics, ed. by P.L. Roe (Academic, London) pp. 245–288

    Google Scholar 

  • Liepmann, H., Roshko, A. (1957): Elements of Gas Dynamics (Wiley, New York)

    Google Scholar 

  • MacCormack, R.W. (1969): “The Effect of Viscosity in Hypervelocity Impact Cratering”, AIAA Paper 69-354

    Google Scholar 

  • Mavriplis, D.J. (1990): AIAA J. 28, 213–221

    Article  ADS  Google Scholar 

  • McDonald, B.E. (1989): J. Comput. Phys. 82, 413–428

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Moretti, G. (1979): Comput. Fluids 7, 191–205

    Article  MathSciNet  MATH  Google Scholar 

  • Morton, K.W., Sweby, P.K. (1987): J. Comput. Phys., 73, 203–230

    Article  MATH  ADS  Google Scholar 

  • Morton, K.W., Paisley, M.F. (1989): J. Comput. Phys. 80, 168–203

    Article  MATH  ADS  Google Scholar 

  • Mulder, W.A. (1985): J. Comput. Phys. 60, 235–252

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Murman, E.M. (1973): Proc. 1st AIAA Comp. Fluid Dyn. Conf. (AIAA, New York) pp. 27–40

    Google Scholar 

  • Napolitano, M. (1986): In 10th Int. Conf. Numer. Methods in Fluid Dynamics, ed. by F.G. Zhuang, Y.L. Zhu, Lecture Notes in Physics, Vol. 264 (Springer, Berlin, Heidelberg), pp. 47–56

    Google Scholar 

  • Ni, R.H. (1982): AIAA J. 20, 1565–1571

    Article  MATH  ADS  Google Scholar 

  • Osher, S., Solomon, F. (1982): Math. Comp. 38, 339–374

    Article  MathSciNet  MATH  Google Scholar 

  • Paul, J.C., LaFond, J.G. (1983): “Analysis and Design of Automobile Forebodies using Potential Flow Theory and a Boundary Layer Separation Criterion”, SAE Paper 830999

    Google Scholar 

  • Peyret, R., Taylor, T.D. (1983): Computational Methods for Fluid Flow, Springer Ser. Comput. Phys. (Springer, Berlin, Heidelberg)

    Google Scholar 

  • Pulliam, T.H., Chaussee, D. (1981): J. Comp. Phys., 39, 347–363

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Pulliam, T.H. (1985): “Implicit Finite Difference Methods for the Euler Equations”, in Recent Advances in Numerical Methods for Fluids, Vol. 4 (Pineridge Press, Swansea)

    Google Scholar 

  • Pulliam, T.H. (1985): In Advances in Computational Transonics, ed. by W.G. Habashi (Pineridge Press, Swansea) pp. 503–542

    Google Scholar 

  • Rackich, J.V., Kutler, P. (1972): “Comparison of Characteristics and Shock Capturing Methods with Application to the Space Shuttle Vehicle”, AIAA Paper 72-191

    Google Scholar 

  • Rai, M.M., Chaussee, D.S. (1984): AIAA J. 22, 1094–1100

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Richtmyer, R.D., Morton, K.W. (1967): Difference Methods for Initial-Value Problems (Interscience, New York)

    MATH  Google Scholar 

  • Rizzi, A. (1981): In Notes on Numerical Fluid Mechanics, Vol. 3, ed. by Rizzi, A., Viviand, H. (Vieweg, Braunschweig)

    Google Scholar 

  • Rizzi, A., Eriksson, L.E. (1982): AIAA J. 20, 1321–1328

    Article  MATH  ADS  Google Scholar 

  • Rizzi, A., Viviand, H. (eds.) (1981): Numerical Methods for the Computation of Inviscid Transonic Flows with Shock Waves, Notes on Numerical Fluid Mechanics, Vol. 3 (Vieweg, Braunschweig)

    Google Scholar 

  • Roe, P.L. (1981): J. Comput. Phys. 43, 357–372

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Roe, P.L. (1986): Annu. Rev. Fluid Mech. 18, 337–365

    Article  MathSciNet  ADS  Google Scholar 

  • Roe, P.L., Baines, M.J. (1982): “Algorithms for Advection and Shock Problems”, in Proc. Fourth GAMM Conf. Numer. Meth. Fluid Mechanics, ed. by H. Viviand (Vieweg, Braunschweig)

    Google Scholar 

  • Rubbert, P.E., Sarris, G.R. (1972): “Review and Evaluation of a Three-Dimensional Lifting Potential Flow Analysis Method for Arbitrary Configurations”, AIAA Paper 72-188

    Google Scholar 

  • Rudy, D.H., Strikwerda, J.C. (1981): Comput. Fluids 9, 327–338

    Article  MATH  Google Scholar 

  • Salas, M., Jameson, A., Melnik, R. (1983): “A Comparative Study of the Nonuniqueness Problem of the Potential Equation”, AIAA Paper 83-1888

    Google Scholar 

  • Sod, G.A. (1978): J. Comput. Phys. 27, 1–31

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Steger, J.L., Pulliam, T.H., Chima, R.V. (1980): “An Implicit Finite Difference Code for Inviscid and Viscous Cascade Flow”, AIAA Paper 80-1427

    Google Scholar 

  • Steger, J.L., Warming, R.F. (1981): J. Comput. Phys. 40, 263–293

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Sweby, P.K. (1984): SIAM J. Numer. Anal. 21, 995–1011

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Thompson, K.W. (1987): J. Comput. Phys. 68, 1–24

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Thompson, K.W. (1990): J. Comput. Phys. 89, 439–461

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Tinoco, E.N., Chen, A.W. (1986): Prog. Astronaut. Aeronaut. 102, 219–255

    Google Scholar 

  • Turkel, E. (1985): In Ninth International Conference on Numerical Methods in Fluid Dynamics, ed. by Soubbaramayer, J.P. Boujot, Lecture Notes in Physics, Vol. 218 (Springer, Berlin, Heidelberg), pp. 571–575

    Google Scholar 

  • Van Leer, B. (1974): J. Comput. Phys. 14, 361–370

    Article  MATH  ADS  Google Scholar 

  • Van Leer, B. (1979): J. Comput. Phys. 32, 101–136

    Article  ADS  Google Scholar 

  • Van Leer, B. (1982): In 8th Int. Conf. Numer. Methods Fluid Dynamics, ed. by E. Krause, Lecture Notes in Physics, Vol. 264 (Springer, Berlin, Heidelberg) pp. 677–683

    Google Scholar 

  • Vinokur, M. (1989): J. Comput. Phys. 81, 1–52

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Viviand, H. (1981): In 7th Int. Conf. Numer. Methods in Fluid Dynamics, ed. by W.C. Reynolds, R.W. MacCormack, Lecture Notes in Physics, Vol. 141 (Springer, Berlin, Heidelberg) pp. 44–54

    Google Scholar 

  • Warming, R.F., Beam, R.M. (1976): AIAA J. 14, 1241–1249

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Woodward, P., Colella, P. (1984): J. Comput. Phys. 54, 115–173

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Yang, J.Y., Lombard, C.K., Bardina, J. (1986): “Implicit Upwind TVD Schemes for the Euler Equations with Bidiagonal Approximate Factorisation”, in Proc. Int. Symp. Comp. Fluid Dynamics, ed. by K. Oshima (Japan Soc. of Comp. Fluid Dynamics, Tokyo) Vol. 1, pp. 174–183

    Google Scholar 

  • Yee, H. (1981): “Numerical Approximation of Boundary Conditions with Application to Inviscid Equations of Gas Dynamics”, NASA TN 81265

    Google Scholar 

  • Yee, H. (1986): In 10th Int. Conf. Numer. Methods in Fluid Dynamics, ed. by F.G. Zhuang, Y.L. Zhu, Lecture Notes in Physics, Vol. 264 (Springer, Berlin, Heidelberg) pp. 677–683

    Google Scholar 

  • Yee, H., Warming, R.F., Harten, A. (1985): J. Comput. Phys. 57, 327–360

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Yee, H., Klopfer, G.H., Montagne, J.L. (1990): J. Comput. Phys. 88, 31–61

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Young, D.P., Melvin, R.G., Bieterman, M.B., Johnson, F.T., Samant, S.S., Bussoletti, J.E. (1990): J. Comput. Phys. (to appear)

    Google Scholar 

  • Yu, N.J., Chen, H.C., Su, T.Y., Kao, T.J. (1990): “Development of a General Multiblock Flow Solver for Complex Configurations”, in Notes Num. Fluid Mech. 29 (Vieweg, Wiesbaden) pp. 603–612

    Google Scholar 

  • Zalesak, S.T. (1979): J. Comput. Phys. 31, 335–362

    Article  MathSciNet  MATH  ADS  Google Scholar 

  • Zalesak, S.T. (1987): Advances in Computer Methods for Partial Differential Equations, VI, eds. R. Vichnevetsky and R.S. Stepleman (IMACS, Rutgers University)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre for Advanced Numerical Computation in Engineering and Science — CANCES, The University of New South Wales, 2052, Sydney, Australia

    Professor Clive A. J. Fletcher

Authors
  1. Professor Clive A. J. Fletcher
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Fletcher, C.A.J. (1991). Inviscid Flow. In: Computational Techniques for Fluid Dynamics 2. Scientific Computation. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58239-4_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-58239-4_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53601-7

  • Online ISBN: 978-3-642-58239-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation