Advertisement

Engineering with Computers

, Volume 24, Issue 1, pp 17–26 | Cite as

Geometry based pre-processor for parallel fluid dynamic simulations using a hierarchical basis

  • Anil Kumar Karanam
  • Kenneth E. JansenEmail author
  • Christian H. Whiting
Original Article

Abstract

The pre-processing stage of finite element analysis of the Navier–Stokes equations is becoming increasingly important as the desire for more general boundary conditions, as well as applications to parallel computers increases. The set up of general boundary conditions and communication structures for parallel computations should be accomplished during the pre-processing phase of the analysis, if possible, to ensure efficient computations for large scale problems in computational fluid dynamics. This paper introduces a general methodology for geometry based boundary condition application and pre-computing of parallel communication tasks.

Keywords

Periodic Boundary Condition Finite Element Mesh Model Entity Natural Boundary Condition Essential Boundary Condition 
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.

Notes

Acknowledgments

This material is based upon work supported by the National Science Foundation under Grant No. 9985340.

References

  1. 1.
    Al-Nasra M, Nguyen DT (1991) An algorithm for domain decomposition in finite element analysis. Comput Struct 39:277–289CrossRefGoogle Scholar
  2. 2.
    Beall MW, Shephard MS (1997) A general topology-based mesh data structure. Int J Numer Method Eng 40(9):1573–1596CrossRefMathSciNetGoogle Scholar
  3. 3.
    Bernard ST, Simon HD (1993) A fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems. In: Proceedings of sixth SIAM conference on parallel processing for scientific computing, pp 711–718Google Scholar
  4. 4.
    Cross M, Walshaw C, Everett M (1997) Mesh partitioning and load-balancing for distributed memory parallel systems. In: Proceedings of international conference on parallel and distributed computing for computational mechanicsGoogle Scholar
  5. 5.
    Dey S (1997) Geometry-based three-dimensional hp-finite element modelling and computations. PhD thesis, Rensselaer Polytechnic InstituteGoogle Scholar
  6. 6.
    Farhat C (1988) A simple and efficient automatic fem domain decomposer. Comput Struct 28:579–602CrossRefGoogle Scholar
  7. 7.
    Farhat C (1989) On mapping of massively parallel processors onto finite element graphs. Comput Struct 32:347–354zbMATHCrossRefGoogle Scholar
  8. 8.
    Gilbert JR, Miller GL, Teng SH (1998) Geometric mesh partitioning: implementation and experiments. SIAM J Sci Comput 19:2091–2110zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Hughes TJR (1987) The finite element method: linear static and dynamic finite element analysis. Prentice-Hall, Englewood CliffszbMATHGoogle Scholar
  10. 10.
    Jansen KE (1999) A stabilized finite element method for computing turbulence. Comput Method Appl Mech Eng 174:299–317zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Jansen KE, Whiting CH, Hulbert GM (1999) A generalized-α method for integrating the filtered Navier–Stokes equations with a stabilized finite element method. Comput Method Appl Mech Eng 190:305–319CrossRefMathSciNetGoogle Scholar
  12. 12.
    Kallinderis Y, Vidwans and Venkatakrishnan A (1994) Parallel dynamic load-balancing algorithm for three-dimensional adaptive unstructured grids. AIAA J 23:497–505Google Scholar
  13. 13.
    Lusk E, Gropp W, Skjellum A (1994) Using MPI—portable parallel programming with the message passing interface. The MIT Press, CambridgeGoogle Scholar
  14. 14.
    O’Bara RM, Beall MW, Shephard MS (2002) Attribute management system for engineering analysis. Eng Comput 18:339–351CrossRefGoogle Scholar
  15. 15.
    Saad Y, Schultz MH (1986) GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput 7:856–869zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Schloegel K, Karypis G, Kumar V (1997) Multilevel diffusion algorithms for repartitioning of adaptive meshes. Technical Report #97-013, University of Minnesota, Department of Computer Science and Army HPC CenterGoogle Scholar
  17. 17.
    Shakib F, Hughes TJR, Johan Z (1989) A multi-element group preconditioned GMRES algorithm for nonsymmetric systems arising in finite element analysis. Comput Method Appl Mech Eng 75:415–456zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Shephard MS (1988) The specification of physical attribute information for engineering analysis. Eng Comput 4:145–155CrossRefGoogle Scholar
  19. 19.
    Shephard MS, Dey S, Flaherty JE (1997) A straight forward structure to construct shape functions for variable p-order meshes. Comput Method Appl Mech Eng 147:209–233zbMATHCrossRefGoogle Scholar
  20. 20.
    Simon HD (1991) Partitioning of unstructured meshes for parallel processing. Comput Syst Eng 2:135–148CrossRefGoogle Scholar
  21. 21.
    Vanderstraeten D, Keunings R (1995) Optimized partitioning of unstructured computational grids. Int J Numer Method Eng 38:433–450zbMATHCrossRefGoogle Scholar
  22. 22.
    Whiting CH, Jansen KE (2001) A stabilized finite element method for the incompressible Navier–Stokes equations using a hierarchical basis. Int J Numer Method Fluids 35:93–116zbMATHCrossRefGoogle Scholar
  23. 23.
    Whiting CH, Jansen KE, Dey S (2003) Hierarchical basis in stabilized finite element methods for compressible flows. Comput Method Appl Mech Eng 192:5167–5185zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2007

Authors and Affiliations

  • Anil Kumar Karanam
    • 1
  • Kenneth E. Jansen
    • 1
    Email author
  • Christian H. Whiting
    • 2
  1. 1.Scientific Computation Research Center, RPITroyUSA
  2. 2.ABAQUS IncProvidenceUSA

Personalised recommendations