Advertisement

Flow Domains and Bases

  • Wolfgang KollmannEmail author
Chapter

Abstract

A set of simple flow domains\(\mathcal{D}\) relevant to turbulent flows and Schauder bases (Sect.  23.8 in Appendix A) for the phase space \(\Omega \) of functions defined on a domain \(\mathcal{D}\) of particular structure and its dual space \(\mathcal{N}\) called test function space are introduced for later use. A fundamental tool for operations in Banach and Hilbert spaces is the notion of a Schauder basis.

References

  1. 1.
    Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. Dover, New York (1972)zbMATHGoogle Scholar
  2. 2.
    Olver, F.W., Lozier, D.W., Boisvert, R.F., Clark, C.W.: NIST Handbook of Mathematical Functions. Cambridge University Press, U.K. (2010)zbMATHGoogle Scholar
  3. 3.
    Batchelor, G.K.: The Theory of Homogeneous Turbulence. Cambridge University Press (1967)Google Scholar
  4. 4.
    Robinson, S.K.: Coherent motions in the turbulent boundary layer. Ann. Rev. Fluid Mech. 23, 601–639 (1991)ADSCrossRefGoogle Scholar
  5. 5.
    Zagarola, M.V., Smits, A.J.: Mean-flow scaling of turbulent pipe flow. JFM 373, 33–79 (1998)ADSCrossRefGoogle Scholar
  6. 6.
    Smits, A.J. (ed.): IUTAM Symposium on Reynolds Number Scaling in Turbulent Flow. Kluwer Academic Publishers, Dordrecht (2004)zbMATHGoogle Scholar
  7. 7.
    McKeon, B.J., Swanson, C.J., Zagarola, M.V., Donnelly, R.J., Smits, A.J.: Friction factors for smooth pipe flow. JFM 511, 41–44 (2004)ADSCrossRefGoogle Scholar
  8. 8.
    Boyd, J.P.: Chebyshev and Fourier Spectral Methods. Dover Publ. Inc., Mineola, New York (2001)zbMATHGoogle Scholar
  9. 9.
    Kollmann, W.: Simulation of vorticity dominated flows using a hybrid approach: i formulation. Comput. Fluids 36, 1638–1647 (2007)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Tsinober, A.: Vortex Stretching versus Production of Strain/Dissipation. In: Hunt, J.C.R., Vasilicos, J.C. (eds.) Turbulence Structure and Vortex Dynamics. Cambridge University Press, Cambridge U.K (2000)zbMATHGoogle Scholar
  11. 11.
    Pileckas, K.: Navier-Stokes system in domains with cylindrical outlets to infinity. In: Friedlander, S., Serre, D. (eds.) Handbook of Mathematical Fluid Dynamics, vol. 4, North Holland, pp. 447–647 (2007)Google Scholar
  12. 12.
    Trefethen, L.N.: Spectral Methods in MATLAB. SIAM (2000). PhiladelphiaGoogle Scholar
  13. 13.
    Loulou, P., Moser, R.D., Mansour, N.N., Cantwell, B.J.: Direct Numerical Simulation of Incompressible Pipe Flow Using a B-spline Spectral Method, p. 110436. NASA Techn, Memor (1997)Google Scholar
  14. 14.
    Botella, O., Shariff, K.: B-spline methods in fluid dynamics. Int. J. Comput. Fluid Dyn. 17, 133–149 (2003)MathSciNetCrossRefGoogle Scholar
  15. 15.
    de Boer, C.: A Practical Guide to Splines, rev edn. Springer, New York (2001)Google Scholar
  16. 16.
    Spalart, P.R., Moser, R.D., Rogers, M.M.: Spectral methods for the navier- stokes equations with one inifinite and two periodic directions. J. Comput. Phys. 96, 297–324 (1991)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    Rogers, M.M., Moser, R.D.: Direct simulation of a self-similar turbulent mixing layer. Phys. Fluids 6, 903–923 (1994)ADSCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of California DavisDavisUSA

Personalised recommendations