Skip to main content

Development of Navier-Stokes Solvers on Hybrid Grids

  • Conference paper
Numerical Flow Simulation III

Summary

The paper presents common developments of solution methods for conservation laws on unstructured, hybrid grids. A time-accurate dual time stepping method for low Mach number flow is presented. A parallel, linear multigrid method has been developed for applications to complex flows. Finally a new approach for generating hybrid grids, based on level set methods is described.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. Karypis et. al. Family of multilevel partitioning algorithms. Online: http://wwwusers.cs.umn.edu/ karypis/metis/ A collection of papers is available online, 1998 – 2001.

    Google Scholar 

  2. E. Turkel: Preconditioned Methods for Solving the Incompressible and Low Speed Compressible Equations, JCP,vol.72, pp 277 – 298, (1987).

    Google Scholar 

  3. A. J. Chorin: A numerical method for solving incompressible viscous flow problems. Journal of Computational Physics, Vol 2, 12–26 (1967).

    Article  MATH  Google Scholar 

  4. M. Breuer, D. Hanel: A Dual Time-Stepping Method for 3-D, Viscous, Incompressible Vortex Flow. Computer & Fluids, vol. 22, pp. 467–484, (1993).

    Article  MATH  Google Scholar 

  5. D. Hanel, A. Dervieux, R. Vilsmeier, O. Gloth, C. Viozat, and L. Fournier. Development of Navier-Stokes solvers on hybrid grids. Notes on Numerical Fluid Mechanics, 66:89– 111, 1998.

    MathSciNet  Google Scholar 

  6. E. Schall, C. Viozat, B. Koobus and A. Dervieux, Computation of low Mach thermical flows with implicit upwind methods, INRIA report, (2002).

    Google Scholar 

  7. D. Hänel, A. Dervieux, O. Gloth, L. Fournier, S. Lanteri, and R. Vilsmeier. Development of Navier-Stokes solvers on hybrid grids. Notes on Numerical Fluid Mechanics, 75:49–66, 2001.

    Google Scholar 

  8. M. H. Lallemand, H. Steve, and A. Dervieux. Unstructured multigridding by volume agglomeration: current status. Computers and Fluids, 21:397–443, 1992.

    Article  MATH  Google Scholar 

  9. D. J. Mavriplis and V. Venkatakrishnan. Agglomeration multigrid solver for two dimensional viscous flows. Int. J. of Comp. Physics, 24:553–570, 1995.

    MATH  Google Scholar 

  10. G. Carré. An implicit multigrid method by agglomeration applied to turbulent flows. Computer & Fluids, 26:299–320, 1997.

    Article  MATH  Google Scholar 

  11. D. J. Mavriplis. Directional agglomeration multigrid techniques for high-Reynolds number viscous flows. ICASE tech. report, 98–6, 1998.

    Google Scholar 

  12. J. Francescatto and A. Dervieux. A semi-coarsening strategy for unstructured multigrid based on agglomeration. Int. J. Numer Meth. in Fluids, 26:927–957, 1998.

    Article  MATH  Google Scholar 

  13. D. J. Mavriplis and V. Venkatalkrishnan. A 3d agglomeration multigrid solver for the Reynolds-average Navier-Stokes equations on unstructure meshes. Int. J. for Num. Meth. in Fluids, 23:527–544, 1996.

    Article  MATH  Google Scholar 

  14. G. Carré and S. Lanteri. Parallel linear multigrid by agglomeration for the acceleration of 3-d compressible flow calculations on unstructured meshes. Numerical Algorithms, 24:309–332, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  15. S. Osher and J.A. Sethian. Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton—Jacobi formulations. J. of Comp. Physics, 79:12–49, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  16. Mulder, Osher, and Sethian. Computing interface motion in compressible gas dynamics. J. Comp. Phys., 100:209–228, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  17. M. Sussman, P. Smereka, and S. Osher. A level set approach for computing solutions to incompressible two-phase flow. J. Comp. Phys., 114:146–159, 1994.

    Article  MATH  Google Scholar 

  18. J. Sethian. Level Set Methods and Fast Marching Methods. Cambridge University Press, 1999.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Häne, D., Dervieux, A., Gloth, O., Fournier, L., Lanteri, S., Vilsmeier, R. (2003). Development of Navier-Stokes Solvers on Hybrid Grids. In: Hirschel, E.H. (eds) Numerical Flow Simulation III. Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM), vol 82. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45693-3_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-45693-3_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-53653-3

  • Online ISBN: 978-3-540-45693-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics