Advertisement

Towards Time-Stable and Accurate LES on Unstructured Grids

  • Frank Ham
  • K. Mattsson
  • Gianluca Iaccarino
  • Parviz Moin
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 56)

Abstract

Control-volume (cv) and node-based (cell-vertex) finite volume discretizations of the incompressible Navier-Stokes equations are compared in terms of accuracy, efficiency, and stability using the inviscid Taylor vortex problem. An energy estimate is shown to exist for both formulations, and stable convective boundary conditions are formulated using the simultaneous approximation term (SAT) method. Numerical experiments show the node-based formulation to be generally superior on both structured Cartesian and unstructured triangular grids, displaying consistent error levels and nearly second-order rates of L 2 velocity error reduction. The cv-formulation, however, out-performs the node-based for the case of Cartesian grids when the Taylor vortices do not cut the boundary.

Keywords

Dirichlet Boundary Condition Energy Estimate Unstructured Grid Unstructured Mesh Cartesian Grid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    R. Mittal and P. Moin. Suitability of upwind-biased finite difference schemes for large-eddy simulation of turbulent flows. AIAA J. 35(8):1415, 1997.zbMATHCrossRefGoogle Scholar
  2. [2]
    F.H. Harlow and J.E. Welch. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surfaces. Phys. Fluids 8:2182, 1965.CrossRefGoogle Scholar
  3. [3]
    B. Perot. Conservation properties of unstructured staggered mesh schemes. J. Comput. Phys. 159:58–89, 2000.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    K. Mahesh, G. Constantinescu, and P. Moin. A numerical method for large-eddy simulation in complex geometries. J. Comput. Phys. 197:215–240, 2004.zbMATHCrossRefGoogle Scholar
  5. [5]
    F. Ham and G. Iaccarino. Energy conservation in collocated discretization schemes on unstructured meshes. Center for Turbulence Research Annual Research Briefs Stanford University, Stanford, California 3–14, 2004.Google Scholar
  6. [6]
    M.H. Carpenter, D. Gottlieb, and S. Abarbanel. Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes. J. Comput. Phys. 111(2), 1994.CrossRefMathSciNetGoogle Scholar
  7. [7]
    P.D. Lax and R.D. Richtmyer. Survey of the Stability of Linear Finite difference Equations. Comm. on Pure and Applied Math. IX, 1956.Google Scholar
  8. [8]
    M.H. Carpenter, D. Gottlieb, and S. Abarbanel. The stability of numerical boundary treatments for compact high-order finite difference schemes. J. Comput. Phys. 108(2), 1993.Google Scholar
  9. [9]
    H.-O. Kreiss and G. Scherer. Finite element and finite difference methods for hyperbolic partial Differential equations. Mathematical Aspects of Finite Elements in Partial Differential Equations., Academic Press, Inc., 1974.Google Scholar
  10. [10]
    G. Strang. Accurate partial difference methods II. Non-linear problems. Num. Math. 6:37–46, 1964.zbMATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    H.-O. Kreiss and L. Wu. On the stability definition of difference approximations for the initial boundary value problems. Appl. Num. Math. 12:212–227, 1993.CrossRefMathSciNetGoogle Scholar
  12. [12]
    K. Mattsson and J. Nordström. Summation by parts operators for finite difference approximations of second derivatives. J. Comput. Phys. 199(2), 2004.Google Scholar
  13. [13]
    J. Nordström, K. Forsberg, C. Adamsson, and P. Eliasson. Finite volume methods, unstructured meshes and strict stability for hyperbolic problems. Appl. Num. Math. 45(4), 2003.Google Scholar
  14. [14]
    B. Gustafsson, H.-O. Kreiss, and J. Oliger. Boundary Procedures for Summation-by-Parts Operators, John Wiley & Sons, Inc., 1995.Google Scholar
  15. [15]
    K. Mattsson. Boundary Procedures for Summation-by-Parts Operators. J. Sci. Comput. 18, 2003.Google Scholar

Copyright information

© Springer 2007

Authors and Affiliations

  • Frank Ham
    • 1
  • K. Mattsson
    • 1
  • Gianluca Iaccarino
    • 1
  • Parviz Moin
    • 1
  1. 1.Center for Turbulence ResearchStanford UniversityStanfordUSA

Personalised recommendations