feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

  • 1
    Electronic Resource
    Electronic Resource
    Journal of scientific computing 15 (2000), S. 265-292 
    ISSN: 1573-7691
    Keywords: finite differences ; corner singularities ; incompressible flows ; adaptive grids ; asymptotic error analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Two problems that include corner singularities are considered. The first concerns the flow of a viscous fluid in a channel driven by a constant pressure gradient, when the velocity satisfies a two-dimensional Poisson equation. The second is Stokes flow in a two-dimensional region when the stream-function satisfies the biharmonic equation. For both problems the boundaries of the domains contain corners. For corner angles greater than some critical value, the stress or the vorticity is singular. Using both a formal analysis and numerical results, we show that numerical approximations for the stream-function and velocity, obtained by using standard second-order finite difference methods, still converge to the exact solutions despite the corner singularities. However, the convergence rate is lower than second-order and the deterioration in the accuracy is not local, i.e., not confined to the corner. On the other hand, even though the vorticity solution of the Stokes problem does not converge, it diverges only locally. At a finite distance from the corner, the vorticity converges with the same rate as the stream-function. Adaptive methods for improving the accuracy are also discussed.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
  • 2
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 713-729 
    ISSN: 0271-2091
    Keywords: finite difference ; boundary conditions ; Navier-Stokes equations ; convergence analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A finite difference method for the Navier-Stokes equations in vorticity -streamfunction formulation is proposed to resolve the difficulty of the lack of a vorticity boundary condition at a no-slip boundary. It is particularly suitable for flows in regions with complicated geometries. Convergence with second-order accuracy in vorticity and velocity is established. In numerical experiments the convergence rates agree with theoretical predictions. Test results for the two-dimensional driven cavity problem and for the flow in expansion and contraction channels are given.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...