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A Comparison Between Domain Decomposition and Fully Implicit Approaches for a Parallel 3D Upwind Flow Solver

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Advances in High Performance Computing

Part of the book series: NATO ASI Series ((ASHT,volume 30))

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Abstract

An implicit method for the solution of the 3D supersonic Euler equations is presented. The numerical technique adopted is a finite volume method based on an unfactored implicit upwind scheme. A great relevance is given to the definition of the implicit operator and to the solution of the linear systems. A preconditioned iterative solver has been used showing better performance than unpreconditioned version. Implementation of the code has been executed on two MIMD supercomputers. The implicit nature of the scheme allows to follow two approaches: a parallel domain decomposition technique and a fully implicit parallel method. Comparisons between the two strategies, in terms of advantages and disadvantages are presented.

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References

  1. Manna, M, (1992) A Three Dimensional High Resolution Compressible Flow Solver, Ph.D. Thesis, VKI, Brussels.

    Google Scholar 

  2. Beam, R, Warming, R.F. (1978) An Implicit Factored Scheme for the Compressible Navier-Stokes Equations, AIAA Journal 16(4).

    Article  Google Scholar 

  3. Fletcher, C.A.J. (1991) Computational Techniques for Fluid Dynamics,Springer-Verlag.

    MATH  Google Scholar 

  4. Dongarra, J., Duff, I., Sorensen, D., Van der Vorst, H. (1991) Solving Linear Systems on Vector and Shared Memory Computers,SIAM, Philadelphia.

    Google Scholar 

  5. Golub, G., van Loan, C. (1990) Matrix computations, The John Hopkins University Press, Baltimore.

    Google Scholar 

  6. Van der Vorst, H. (1992) Bi-CGSTAB: A Fast and Smoothly Converging Variant of the Bi-CG for the Solution of Non symmetric Linear Systems, SIAM Journal 13(2), 631–644.

    MATH  Google Scholar 

  7. Stella, F., Bucchignani, E. (1996) A true transient vorticity-velocity method using preconditioned Bi-CGSTAB, Numerical heat transfer (in press).

    Google Scholar 

  8. Iaccarino, G. (1993) Soluzione Numerica delle Equazioni di Eulero: Acceleratori di Convergenza per Solutori di Tipo Upwind, Master Thesis, University of Napoli.

    Google Scholar 

  9. Bucchignani, E., Stella, F. (1995) A Fully Implicit Parallel Solver for Viscous Flows: Numerical Tests on High Performance Machines, in Ecer A. et al. (Ed.), Parallel Computational Fluid Dynamics: Implementations and Results Using Parallel Computers, 569–576, Elsevier, Amsterdam.

    Google Scholar 

  10. Saad, Y. (1992) Numerical methods for large eigenvalue problems, Manchester University Press, Manchester.

    MATH  Google Scholar 

  11. Pandolfi, M., Borrеlli, S. (1991) An Upwind Formulation for Hypersonic Non Equilibrium Flows, in: Modern Research Topics in Aerospace Propulsion, Springer & Verlag.

    Google Scholar 

  12. Hirsch, C. (1991) Numerical Computation of Internal and External Flows I, John Wiley and Sons, New York.

    Google Scholar 

  13. Roe, P. (1981) Approximate Riemann Solvers, Parameter Vectors and Difference Schemes, J. Corp. Physics 43, 357–372.

    Article  MathSciNet  MATH  Google Scholar 

  14. Osher, S., Solomon, F. (1982) Upwind Difference Schemes for Hyperbolic Systems of Conservation Laws, Mathematics of Computations 38(158), 339–374.

    Article  MathSciNet  MATH  Google Scholar 

  15. Venkatakrishnan, V. (1991) Preconditioned Conjugate Gradient Methods for the Compressible Navier- Stokes Equations, AIAA Journal 29(7) 1092–1100.

    Article  Google Scholar 

  16. Quarteroni, A. (1992) Modelli Matematici e Numerici per la Fluidodinamica, Scuola Normale Supeгiore di Pisa.

    Google Scholar 

  17. Brussino, G., Sonnad V. (1989) A Comparison of Direct and Preconditioned Iterative Techniques for Sparse, Unsymmetric Systems of Linear Equations, Int. J. Num. Meth. in Engineering 28, 801–815.

    Article  Google Scholar 

  18. Sonneveld, P. (1989) CGS, a fast Lanczos type solver for nonsymmetric linear systems, SIAM J. Sci. Stat. Computing 10(1), 36–52.

    Article  MathSciNet  MATH  Google Scholar 

  19. Ralston, A., Rabinowitz, P. (1978) A first course in numerical analysis, McGraw-Hill International Editions.

    MATH  Google Scholar 

  20. Borrelli, S., Matrone, A., Schiano, P. (1992) A Multibock Hypersonic Flow Solver for Massively Parallel Computer, in: Pelz R.B. et al (Ed.), Parallel Computational Fluid Dynamics ‘82,25–37, North-Holland, Amsterdam.

    Google Scholar 

  21. Tromeur-Dervot, D., Roux, F. (1993) Parallelization via domain decomposition techniques of Multigrid and ADI solvers for Navier-Stokes Equations, in: Ecer A. et al. (Ed.) Parallel Computational Fluid Dynamics: New Trends and Advances, 349–356, Elsevier, Amsterdam.

    Google Scholar 

  22. Schreck, E., Peric, M. (1993) Computation of fluid flow with a parallel multigrid solver, Int. J. Num. Meth. Fluids 16, 303–327.

    Article  MATH  Google Scholar 

  23. Stella, F., Marrone, M., Bucchignani, E. (1993) A Parallel Preconditioned CG Type method for Incompressible Naviет-Stokes Equations, in: Ecer A. et al. (Ed.) Parallel Computational Fluid Dynamics: New Trends and Advances, 325–332, Elsevier, Amsterdam.

    Google Scholar 

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© 1997 Springer Science+Business Media Dordrecht

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Bucchignani, E., Iaccarino, G. (1997). A Comparison Between Domain Decomposition and Fully Implicit Approaches for a Parallel 3D Upwind Flow Solver. In: Grandinetti, L., Kowalik, J., Vajtersic, M. (eds) Advances in High Performance Computing. NATO ASI Series, vol 30. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5514-4_8

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  • DOI: https://doi.org/10.1007/978-94-011-5514-4_8

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6322-7

  • Online ISBN: 978-94-011-5514-4

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