Skip to main content
SpringerLink
Log in

Development of a Variational Multiscale Large-Eddy Simulation Code ‘MISTRAL’ Using Double-Scale Finite Elements

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

Abstract

A variational multiscale large-eddy simulation (VMS-LES) code, named MISTRAL, has been developed based upon the finite element method (FEM) for accurate and practical computation of geometrically complicated turbulent flow problems. The numerical strategy of the FEM-based VMS-LES is explained, especially focusing on the double-scale approximation for velocity and pressure in the incompressible Navier-Stokes equations, a pressure stabilization technique and a multiscale turbulence modeling. A unique technique is also employed in the time integration to realize an efficient inversion of the multiscale mass matrix and to form the multiscale pressure Poisson equation used in the approximate projection method for divergence-free constraint of velocity. As a numerical demonstration, a 2D driven cavity flow problem has been solved with the MISTRAL code in a wide range of Reynolds number (Re=1000 to 50000). The results are compared with reference data to quantitatively estimate the accuracy (magnitude of errors in terms of L 2 norms) of the proposed VMS-LES 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. Hughes, T.J.R., Mazzei, L., Jansen, K.E.: Large eddy simulation and the variational multiscale method. Comput. Vis. Sci. 3, 47–59 (2000)

    Article  MATH  Google Scholar 

  2. Collis, S.: Monitoring unresolved scales in multiscale turbulence modeling. Phys. Fluids 13, 1800–1806 (2001)

    Article  Google Scholar 

  3. Hughes, T.J.R., Mazzei, L., Oberai, A.A.: The multiscale formulation of large eddy simulation: Decay of homogeneous isotropic turbulence. Phys. Fluids 13, 505–512 (2001)

    Article  Google Scholar 

  4. Hughes, T.J.R., Oberai, A.A., Mazzei, L.: Large eddy simulation of turbulent channel flows by the variational multiscale method. Phys. Fluids 13, 1784–1799 (2001)

    Article  Google Scholar 

  5. Erturk, E., Gökçöl, C.: Fourth-order compact formulation of Navier–Stokes equations and driven cavity flow at high Reynolds numbers. Int. J. Numer. Meth. Fluids. 50, 421–436 (2006)

    Article  MATH  Google Scholar 

  6. Hughes, T.J.R., Franca, L.P.: A new finite element formulation for computational fluid dynamics: VII The Stokes problem with various well-posed boundary conditions: Symmetric formulations that converge for all velocity/pressure spaces. Comput. Methods Appl. Mech. Eng. 65, 85–96 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  7. Silvester, D.J., Kechkar, N.: Stabilised bilinear-constant velocity-pressure finite elements for the conjugate gradient solution of the Stokes problem. Comput. Methods Appl. Mech. Eng. 79, 71–86 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  8. Eguchi, Y.: A new positive-definite regularization of incompressible Navier-Stokes equations discretized with Q1/P0 finite element. Int. J. Numer. Meth. Fluids 41, 881–904 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  9. Brooks, A.N., Hughes, T.J.R.: Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Eng. 32, 199–259 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  10. Eguchi, Y.: On streamline diffusion arising in Galerkin FEM with predictor/multi-corrector time integration. Int. J. Numer. Meth. Fluids 39, 1037–1052 (2002)

    Article  MATH  Google Scholar 

  11. Eguchi, Y.: Practical techniques for a 3-D FEM analysis of incompressible fluid flow contained with slip walls and a downstream tube bundle. Int. J. Numer. Meth. Fluids 37, 279–295 (2001)

    Article  MATH  Google Scholar 

  12. Almgren, A.S., Bell, J.B., Crutchfield, W.: Approximate projection methods: Part 1. inviscid analysis. SIAM J. Sci. Comput. 22, 1139–1159 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  13. Stevens, D.E., Chan, S.T., Gresho, P.M.: An approximate projection method for incompressible flow. Int. J. Numer. Meth. Fluids 40, 1303–1325 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  14. Kraichnan, R.H.: Eddy viscosity in two and three dimensions. J. Atmos. Sci. 33, 1521–1536 (1976)

    Article  Google Scholar 

  15. Sukoriansky, S., Chekhlov, A., Orszag, S.A., Galperin, B., Staroselsky, I.: Large eddy simulation of two-dimensional isotropic turbulence. J. Sci. Comput. 11, 13–45 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  16. Su, W.-D., Zhao, H., Cai, Q.-D., Xiong, A.-K., Wu, J.-Z.: A diagnosis of linear eddy-viscosity in turbulence modeling. Phys. Fluids 14, 1284–1287 (2002)

    Article  Google Scholar 

  17. Hatayama, S.: Parallel computations of incompressible viscous flow in a lid-driven square cavity and program performance on the NWT computer system. Technical Report Of National Aerospace Laboratory TR-1363T (NALTR0001363T). (As of Nov. 2007, the report is available at http://send.chofu.jaxa.jp/send/jpn/dlpdf.php3/naltr0001363t.pdf?id=NALTR0001363T) (1998)

Download references

Author information

Authors and Affiliations

  1. Fluid Dynamics Sector, The Central Research Institute of Electric Power Industry, Abiko, Japan

    Yuzuru Eguchi

Authors
  1. Yuzuru Eguchi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuzuru Eguchi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Eguchi, Y. Development of a Variational Multiscale Large-Eddy Simulation Code ‘MISTRAL’ Using Double-Scale Finite Elements. J Sci Comput 43, 433–453 (2010). https://doi.org/10.1007/s10915-008-9226-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10915-008-9226-4

Keywords

Search

Navigation