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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Manna, M, (1992) A Three Dimensional High Resolution Compressible Flow Solver, Ph.D. Thesis, VKI, Brussels.
Beam, R, Warming, R.F. (1978) An Implicit Factored Scheme for the Compressible Navier-Stokes Equations, AIAA Journal 16(4).
Fletcher, C.A.J. (1991) Computational Techniques for Fluid Dynamics,Springer-Verlag.
Dongarra, J., Duff, I., Sorensen, D., Van der Vorst, H. (1991) Solving Linear Systems on Vector and Shared Memory Computers,SIAM, Philadelphia.
Golub, G., van Loan, C. (1990) Matrix computations, The John Hopkins University Press, Baltimore.
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.
Stella, F., Bucchignani, E. (1996) A true transient vorticity-velocity method using preconditioned Bi-CGSTAB, Numerical heat transfer (in press).
Iaccarino, G. (1993) Soluzione Numerica delle Equazioni di Eulero: Acceleratori di Convergenza per Solutori di Tipo Upwind, Master Thesis, University of Napoli.
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.
Saad, Y. (1992) Numerical methods for large eigenvalue problems, Manchester University Press, Manchester.
Pandolfi, M., Borrеlli, S. (1991) An Upwind Formulation for Hypersonic Non Equilibrium Flows, in: Modern Research Topics in Aerospace Propulsion, Springer & Verlag.
Hirsch, C. (1991) Numerical Computation of Internal and External Flows I, John Wiley and Sons, New York.
Roe, P. (1981) Approximate Riemann Solvers, Parameter Vectors and Difference Schemes, J. Corp. Physics 43, 357–372.
Osher, S., Solomon, F. (1982) Upwind Difference Schemes for Hyperbolic Systems of Conservation Laws, Mathematics of Computations 38(158), 339–374.
Venkatakrishnan, V. (1991) Preconditioned Conjugate Gradient Methods for the Compressible Navier- Stokes Equations, AIAA Journal 29(7) 1092–1100.
Quarteroni, A. (1992) Modelli Matematici e Numerici per la Fluidodinamica, Scuola Normale Supeгiore di Pisa.
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.
Sonneveld, P. (1989) CGS, a fast Lanczos type solver for nonsymmetric linear systems, SIAM J. Sci. Stat. Computing 10(1), 36–52.
Ralston, A., Rabinowitz, P. (1978) A first course in numerical analysis, McGraw-Hill International Editions.
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.
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.
Schreck, E., Peric, M. (1993) Computation of fluid flow with a parallel multigrid solver, Int. J. Num. Meth. Fluids 16, 303–327.
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
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
Download citation
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
eBook Packages: Springer Book Archive