zbMATH — the first resource for mathematics

A parallel Newton-Krylov method for Navier-Stokes rotorcraft codes. (English) Zbl 1161.76553
Summary: The application of Krylov subspace iterative methods to unsteady three-dimensional Navier-Stokes codes on massively parallel and distributed computing environments is investigated. Previously, the Euler mode of the Navier-Stokes flow solver Transonic Unsteady Rotor Navier-Stokes (TURNS) has been coupled with a Newton-Krylov scheme which uses two Conjugate-Gradient-like (CG) iterative methods. For the efficient implementation of Newton-Krylov methods to the Navier-Stokes mode of TURNS, efficient preconditioners must be used. Parallel implicit operators are used and compared as preconditioners. Results are presented for two-dimensional and three-dimensional viscous cases. The Message Passing Interface (MPI) protocol is used, because of its portability to various parallel architectures.

76M99 Basic methods in fluid mechanics
76U05 General theory of rotating fluids
65F10 Iterative numerical methods for linear systems
65Y05 Parallel numerical computation
Full Text: DOI
[1] Anderson W.K. Newman J.C. III Whitfield D.L. Nielson E.J. 1999 Sensitivity analysis for the Navier–Stokes equations on unstructured meshes using complex variables AIAA Paper 99 3294
[2] Beam R. Warming R.F. 1977 An implicit factored scheme for the compressible Navier–Stokes equations AIAA Paper 77 645 · Zbl 0374.76025
[3] Candler G.V. Wright M.J. McDonald J.D. 1994 A data parallel LU-SGS method for reacting flows AIAA Journal 32 2380 2386 · Zbl 0824.76061
[4] Ekici K. Parallel computing techniques for rotorcraft aerodynamics PhD Thesis, School of Aeronautics and Astronautics, Purdue University West Lafayette, IN
[5] Ekici K. Lyrintzis A.S. 2000 Parallel computing techniques for rotorcraft aerodynamics AIAA Paper 2000 2617
[6] Ekici K. Lyrintzis A.S. 2001 Parallel Newton–Krylov methods for rotorcraft aerodynamics AIAA Paper 2001 2587
[7] Ekici K. Lyrintzis A.S. 2002 Parallelization of rotorcraft aerodynamics Navier–Stokes equations AIAA Journal 40 887 896
[8] Keyes, D.E., Kaushik, D.K. and Smith, B.F. (1997). ”Prospects for CFD on petaflops systems”,ICASE Report · Zbl 0990.76074
[9] MacCormack R.W. 1985 Current status of numerical solutions of the Navier–Stokes equations AIAA Paper 85 0032
[10] McHugh P.R. Knoll D.A. 1993 Inexact Newton’s method solutions to the incompressible Navier–Stokes and energy equations using standard and matrix-free implementations AIAA Paper 93 3332
[11] Newman III, J.C., Anderson, W.K. and Whitfield, D.L. (1998) ”Multidisciplinary Sensitivity Derivatives Using Complex Variables”, MSSU-EIRS-ERC 98-08, NSF Engineering Research Center for Computational Field Stimulation, MS.
[12] Newman J.C. III Whitfield D.L. Anderson W.K. 1999 A step-size independent approach for multidisciplinary sensitivity analysis and design optimization AIAA Paper 99 3101
[13] Nielson, E.J., Anderson, W.K., Walters, R.W. and Keyes, D.E. (1995) ”Application of Newton–Krylov Methodology to a Three-Dimensional Unstructured Euler Code”, AIAA TR-95-1733.
[14] Saad Y. 1996 Iterative Methods for Sparse Linear Systems PWS Publishing Company Boston, MA · Zbl 1031.65047
[15] Saad Y. Shultz M. 1986 GMRES: a generalized minimal residual algorithm for solving nonsymmetric systems SIAM Journal on Scientific and Statistical Computing 7 856 869 · Zbl 0599.65018
[16] Srinivasan G.R. Baeder J.D. 1993 TURNS: a free-wake Euler/Navier–Stokes numerical method for helicopter rotors AIAA Journal 31 959 962
[17] Srinivasan G.R. Sankar L.N. 1995 Status of Euler and Navier–Stokes CFD methods for helicopter applications Proceedings of the 2nd AHS International Aeromechanics Specialists’ Conference 2 6-1–6-19
[18] Srinivasan G.R. Baeder J.D. Obayashi S. McCroskey W.J. 1992 Flowfield of a lifting rotor in Hover: a Navier–Stokes simulation AIAA Journal 30 2371 2378 · Zbl 0760.76065
[19] Srinivasan G.R. Raghavan V. Duque E.P.N. McCroskey W.J. 1993 Flowfield analysis of modern helicopter rotors in Hover by Navier–Stokes method Journal of the American Helicopter Society 38 3 10
[20] Tidriri M.D. 1995 Krylov Methods for Compressible Flows, ICASE Report 95-48 NASA Langley Research Center Hampton, VA
[21] Wissink A.M. Efficient parallel implicit methods for rotary-wing calculations PhD Thesis, Department of Aerospace Engineering and Engineering Mechanics, University of Minnesota Minneapolis, MN
[22] Wissink A.M. Lyrintzis A.S. Chronopoulos A.T. 1996a Efficient iterative methods applied to the solutions of transonic flows Journal of Computational Physics 123 379 396 · Zbl 0849.76057
[23] Wissink A.M. Lyrintzis A.S. Strawn R.C. 1996b Parallelization of a three-dimensional flow solver for Euler rotorcraft aerodynamics AIAA Journal 34 2276 2283 · Zbl 0911.76050
[24] Wissink A.M. Lyrintzis A.S. Chronopoulos A.T. 1999 Parallel Newton–Krylov method for rotary-wing flowfield calculations AIAA Journal 37 1213 1221
[25] Wright M.J. Candler G.V. Prampolini M. 1996 A data-parallel LU relaxation method for the Navier–Stokes equations AIAA Journal 34 1371 1378 · Zbl 0902.76084
[26] Wright M.J. Candler G.V. Bose D. 1998 Data-parallel line relaxation method for Navier–Stokes equations AIAA Journal 36 1603 1609
[27] Yoon S. Jameson A. 1988 Lower–upper symmetric Gauss–Seidel method for the Euler and Navier–Stokes equations AIAA Journal 26 1025 1026
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.