Skip to main content
SpringerLink
Log in

Stabilization Methods for Spectral Element Computations of Incompressible Flows

  • Published:
Journal of Scientific Computing Aims and scope Submit manuscript

Abstract

A stabilization method for the spectral element computation of incompressible flow problems is investigated. It is based on a filtering procedure which consists in filtering the velocity field by a spectral vanishing Helmholtz-type operator at each time step. Relationship between this filtering procedure and SVV-stabilization method, introduced recently in [JCP, 2004, 196(2), p680], is established. A number of numerical examples are presented to show the accuracy and stabilization capability of the method.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Boyd J.P. (1998). Two comments on filtering (artificial viscosity) for Chebyshev and Legendre spectral and spectral element methods: Preserving the boundary conditions and interpretation of the filter as a diffusion. J. Comput. Phys. 143: 283–288

    Article  MathSciNet  MATH  Google Scholar 

  2. Fischer P., Mullen J. (2001). Filter-based stabilization of spectral element methods. C. R. Acad. Sci. Paris 332(1): 265–270

    MathSciNet  Google Scholar 

  3. Guermond J.L., Shen J. (2004). On the error estimates for the rotational pressure-correction projection methods. Math.Comp. 73: 1719–1737

    Article  MathSciNet  Google Scholar 

  4. Huang F.H., Xu C.J. (2005). On the error estimates for the rotational pressure-correction projection spectral methods for the unsteady Stokes equations. J. Comput.Math. 23(3): 285–304

    MathSciNet  Google Scholar 

  5. Kaber O.S.M. (1996). A Legendre pseudospectral viscosity method. J. Comput. Phys. 128: 165–180

    Article  MATH  MathSciNet  Google Scholar 

  6. Karamanos G.S., Karniadakis G.E. (2000). A spectral vanishing viscosity method for large-eddy simulation. J. Comput. Phys. 163: 22–50

    Article  ADS  MathSciNet  Google Scholar 

  7. Maday Y., Kaber O.S.M., Tadmor E. (1993). Legendre pseudo-spectral viscosity method for nonlinear conservation laws. SIAM J. Numer. Anal. 30(2): 321–342

    Article  MathSciNet  Google Scholar 

  8. Maday Y., Patera A.T. (1988). Spectral element methods for the Navier–Stokes equations. In: Noor A.K. (eds). State-of-the-Art Surveys in Computational Mechanics. ASME, New York, pp. 71–143

    Google Scholar 

  9. Pasquetti R., Xu C.J. (2002). High-order algorithms for large eddy simulation of incompressible flows. J. Sci. Comp. 17(1–4): 273–284

    Article  MathSciNet  Google Scholar 

  10. Pasquetti R., Xu C.J. (2002). Comments on “Filter-based stabilization of spectral element methods”. J. Comput. Phys. 182: 646–650

    Article  ADS  MathSciNet  Google Scholar 

  11. Qian L., Vezza M. (2001). A Vorticity-based method for incompressible unsteady viscous flows. J. Comput. Phys. 172: 515–542

    Article  ADS  CAS  MathSciNet  Google Scholar 

  12. Tadmor E. (1989). Convergence of spectral methods for nonlinear conservation laws. SIAM J. Numer. Anal. 26(1): 30–44

    Article  MATH  MathSciNet  Google Scholar 

  13. Xu C.J., Pasquetti R. (2001). On the efficiency of semi-implicit and semi-Lagrangian spectral methods for the calculation of incompressible flows. Inter. J. Numer. Meth. Fluids 35: 319–340

    Article  CAS  Google Scholar 

  14. Xu C.J., Pasquetti R. (2004). Stabilized spectral element computations of high Reynolds number incompressible flows. J. Comput. Phys. 196(2): 680–704

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Xiamen University, Xiamen, China

    Chuanju Xu

Authors
  1. Chuanju Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chuanju Xu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xu, C. Stabilization Methods for Spectral Element Computations of Incompressible Flows. J Sci Comput 27, 495–505 (2006). https://doi.org/10.1007/s10915-005-9059-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10915-005-9059-3

Keywords

Search

Navigation