Skip to main content

Methods for Solving Viscous Incompressible Flow Problems

  • Chapter
  • First Online:
Computation of Viscous Incompressible Flows

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

  • 1939 Accesses

Abstract

In this chapter, numerical solution approaches for viscous incompressible flow are briefly compared. Detailed discussions of each approach follow in separate chapters. All discussions are from an engineering perspective and mathematical formalities are not emphasized, in keeping with our perspective for this monograph that CFD is an engineering tool for supporting mission tasks, and thus one can implement well-founded numerical algorithms and physical models to resolve engineering issues at hand. To make significant impacts on missions such as aerospace vehicle design and operation, the CFD applications procedure is just as important as tool development. Here, we present a quick summary of numerical approaches most suitable for application to tasks for supporting missions, especially space exploration missions.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

References

  • Choi, D., Merkle, C. L.: Application of time-iterative schemes to incompressible flow. AIAA J., 23, No. 10, 1518–1524 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  • Chorin, A. J.: A numerical method for solving incompressible viscous flow problems. J. Comp. Phys., 2, 12–26 (1967)

    Article  MATH  Google Scholar 

  • Chorin, A. J.: Numerical solution of Navier-Stokes equations. Math. Comput., 22, No. 104, 745–762 (1968)

    Article  MATH  MathSciNet  Google Scholar 

  • Dennis, S. C. R., Ingham, D. B., Cook, R. N.: Finite-difference methods for calculating/steady incompressible flows. J. Comp. Phys., 33, 325–339 (1979)

    Article  MATH  Google Scholar 

  • Fasel, H.: Investigation of the stability of boundary layers by a finite-difference model of the Navier-Stokes equations, Part II. J. Fluid Mech. 78, 355–383 (1972)

    Article  Google Scholar 

  • Ferziger, J. H.: Incompressible turbulent flows. J. Comp. Phys., 69, 1–48 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  • Ferziger, J. H., Peric, M.: Computational Methods for Fluid Dynamics, 3rd edn., Springer, Berlin (2002)

    MATH  Google Scholar 

  • Gatski, T. B., Grosch, C. E., Rose, M. E.: A numerical study of the two-dimensional Navier-Stokes equations in vorticity-velocity variables. J. Comp. Phys., 48, 1–22 (1982)

    Article  MATH  Google Scholar 

  • Gresho, M. P., Sani, R. L.: On pressure boundary conditions for the incompressible Navier-Stokes equations. Int. J. Num. Methods Fluids, 7, 1111–1145 (1987)

    Article  MATH  Google Scholar 

  • Issa, R. I.: Solution of the implicitly discretized fluid flow equations by operator-splitting. J. Comp. Phys., 62, 40–65 (1985)

    Article  MathSciNet  Google Scholar 

  • Kwak, D., Chang, J. L. C., Shanks, S. P., Chakravarthy, S.: A three-dimensional incompressible Navier-Stokes flow solver using primitive variables. AIAA J., 24, No. 3, 390–396 (1986) (Original version: AIAA Paper 84-0253, AIAA 22nd Aerospace Sciences Meeting, Reno, Nevada, Jan. 9–12 (1984)

    Article  MATH  Google Scholar 

  • Marchuk, G. M.: Methods of Numerical Mathematics, Springer, Berlin (1975)

    MATH  Google Scholar 

  • Orszag, S. A., Israeli, M., Deville, M. O.: Boundary conditions for incompressible flows. J. Sci. Comput., 1, 75–111 (1986)

    Article  MATH  Google Scholar 

  • Patankar, S. V.: Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Co., New York (1980)

    MATH  Google Scholar 

  • Patankar, S. V., Ivanovic, M., Sparrow, E. M.: Analysis of turbulent flow and heat transfer in internally finned tubes and annuli. Int. J. Heat Mass Transf., 101, 9929–9937 (1979)

    Google Scholar 

  • Quartapelle, L.: Numerical Solution of the Incompressible Navier-Stokes Equations, Birkhauser, Basel (1993)

    MATH  Google Scholar 

  • Steger, J. L., Kutler, P.: Implicit finite-difference procedures for the computation of vortex wakes. AIAA J., 15, No. 4, 581–590 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  • Temam, R.: Navier Stokes Equations, Revised edn., North Holland, Amsterdam (1979)

    MATH  Google Scholar 

  • Yanenko, N. N.: The Method of Fractional Steps, Springer, Berlin (1971)

    MATH  Google Scholar 

  • Caretto, L. S., Gosman, A. D., Patankar, S. V., Spalding, D. B.: Two calculation procedures for steady three-dimensional flows with recirculation. Proceeding of the 3rd International Conference on Numerical Methods in Fluid Dynamics, Paris, France (1972)

    Google Scholar 

  • Chang, J. L. C., Kwak, D.: On the method of pseudo compressibility for numerically solving incompressible flows. AIAA Paper 84-0252 (1984)

    Google Scholar 

  • Dwyer, H. S., Soliman, M., Hafez, M.: Time accurate solutions of the Navier-Stokes equations for reacting flows. Proceeding of the 10th International Conference on Numerical Methods in Fluid Dynamics, Beijing, China, Springer, Berlin, pp. 247–251 (1986)

    Google Scholar 

  • Hafez, M., Dacles, J., Soliman, M.: A velocity vorticity method for viscous incompressible flow calculations. Proceedings of the 11th International Conference on Numerical Methods in Fluid Dynamics, Williamsburg, Virginia, June 27–July 1 (1988)

    Google Scholar 

  • Kiris, C., Kwak, D.: Numerical solution of incompressible Navier-Stokes equations using a fractional-step approach. Comp. Fluids, 30, 829–851 (2001) (Original version in AIAA Paper 96-2089)

    Google Scholar 

  • Kwak, D.: Computation of viscous incompressible flows. von Karman Institute for Fluid Dynamics, Lecture Series 1989–04 (1989) (Also NASA TM 101090, March 1989)

    Google Scholar 

  • Merkle, C. L., Athavale, M.: Time-accurate unsteady incompressible flow algorithms based on artificial compressibility. AIAA Paper 87-1137 (1987)

    Google Scholar 

  • Osswald, G., Ghia, K. N., Ghia, U.: Direct algorithm for solution of incompressible three-dimensional unsteady Navier-Stokes equations. AIAA Paper 87-1139 (1987)

    Google Scholar 

  • Chang, J. L. C., Kwak, D., Dao, S. C.: A three dimensional incompressible flow simulation method and its application to the Space Shuttle main engine – Part I, Laminar Flow. AIAA Paper 85-0175 (1985a)

    Google Scholar 

  • Chang, J. L. C., Kwak, D., Dao, S. C., Rosen, R.: A three dimensional incompressible flow simulation method and its application to the Space Shuttle main engine – Part II, Turbulent Flow. AIAA Paper 85-1670 (1985b)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dochan Kwak .

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media B.V.

About this chapter

Cite this chapter

Kwak, D., Kiris, C.C. (2011). Methods for Solving Viscous Incompressible Flow Problems. In: Computation of Viscous Incompressible Flows. Scientific Computation. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0193-9_2

Download citation

  • DOI: https://doi.org/10.1007/978-94-007-0193-9_2

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-0192-2

  • Online ISBN: 978-94-007-0193-9

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics