Advertisement

Appendix D: Green’s Function for Periodic Pipe Flow

  • Wolfgang KollmannEmail author
Chapter

Abstract

The Navier–Stokes equations governing the flow of a single incompressible fluid contain the pressure gradient as the local effect of the surface force per unit area. It is straightforward to derive the Poisson pde for the pressure and the associated boundary conditions. The Green’s function is one of the methods to solve the Poisson pde for the pressure and thus eliminate the pressure from the Navier–Stokes equations.

References

  1. 1.
    Boyd, J.P.: Chebyshev and Fourier Spectral Methods. Dover Publ. Inc., Mineola, New York (2001)zbMATHGoogle Scholar
  2. 2.
    Kollmann, W.: Simulation of vorticity dominated flows using a hybrid approach: i formulation. Comput. Fluids 36, 1638–1647 (2007)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. Dover, New York (1972)zbMATHGoogle Scholar
  4. 4.
    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
  5. 5.
    Majda, A.J., Bertozzi, A.L.: Vorticity and Incompressible Flow. Cambridge University Press, Cambridge, U.K. (2002)zbMATHGoogle Scholar
  6. 6.
    Canuto, C., Hussaini, M.Y., Zang, T.A.: Spectral Methods in Fluid Dynamics. Springer, Berlin (1988)CrossRefGoogle Scholar
  7. 7.
    Hartmann, P.: Ordinary Differential Equations. SIAM, Philadelphia (2002)CrossRefGoogle Scholar
  8. 8.
    Duffy, D.G.: Greenś Functions with Applications. Chapman & Hall/CRC, Boca Raton, Florida (2001)CrossRefGoogle Scholar
  9. 9.
    Constantin, P., Foias, C.: Navier-Stokes Equations. University of Chicago Press (1988)Google Scholar
  10. 10.
    Constantin, P.: Euler equations, navier-stokes equations and turbulence. In: Mathematical Foundation of Turbulent Viscous Flows. Lecture Notes in Mathematics, vol. 1871, pp. 1–43 (2006)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of California DavisDavisUSA

Personalised recommendations