303
Views
16
CrossRef citations to date
0
Altmetric
Original Articles

Solution of linear systems in Fourier-based methods for aircraft applications

, , &
Pages 79-87 | Received 30 May 2012, Accepted 12 Nov 2012, Published online: 28 Jan 2013

References

  • Badcock, K.J., Richards, B., and Woodgate, M., 2000. Elements of computational fluid dynamics on block structured grids using implicit solvers, Progress in Aerospace Sciences 31 (5–6) (2000), pp. 351–392. DOI: 10.1016/S0376-0421(00)00005-1
  • Badcock, K.J., and S. Timme, S. Marques, H. Khodaparast, M. Prandina, J. E. Mottershead, A. Swift, A. Da Ronch, and M. A. Woodgate, , 2011. Transonic aeroelastic simulation for instability searches and uncertainty analysis, Progress in Aerospace Sciences 47 (5) (2011), pp. 392–423. DOI: 10.1016/j.paerosci.2011.05.002
  • Benzi, M., 2002. Preconditioning techniques for large linear systems: a survey, Journal of Computational Physics 182 (2) (2002), pp. 418–477. DOI: 10.1006/jcph.2002.7176
  • Bruaset, A.M., Tveito, A., and Winther, R., 1990. On the stability of relaxed incomplete LU factorizations, Mathematics of Computation 54 (1990), pp. 701–719.
  • Chow, E., and Saad, Y., 1997. Experimental study of ILU preconditioners for indefinite matrices. Minneapolis, MN: Supercomputing Institute; 1997, Technical report UMSI 97/95.
  • Custer, C.H., 2009. A nonlinear harmonic balance solver for an implicit CFD code: OVERFLOW 2. Duke University; 2009, Thesis (PhD). Department of Mechanical Engineering and Materials Science.
  • Da Ronch, A., 2012. On the calculation of dynamic derivatives using computational fluid dynamics. Liverpool, UK: University of Liverpool; 2012, Thesis (PhD). School of Engineering.
  • Da Ronch, A., Ghoreyshi, M., and Badcock, K.J., 2011a. On the generation of flight dynamics aerodynamic tables by computational fluid dynamics, Progress in Aerospace Sciences 47 (8) (2011a), pp. 597–620. DOI: 10.1016/j.paerosci.2011.09.001
  • Da Ronch, A., and McCracken, A.J., Badcock, K.J., Widhalm, M., and Campobasso, M.S.,, , 2011b. Linear frequency domain and harmonic balance predictions of dynamic derivatives. Accepted for publication in, Journal of Aircraft (2011b), See also AIAA Paper 2010–4699.
  • Da Ronch, A., and Vallespin, D., Ghoreyshi, M., and Badcock, K.J, , 2012. Evaluation of dynamic derivatives using computational fluid dynamics, AIAA Journal 50 (2) (2012), pp. 470–484. DOI: 10.2514/1.J051304
  • Eisenstat, S.C., Elman, S.C., and Schultz, M., 1983. Variational iterative methods for nonsymmetric systems of linear equations, SIAM, Journal of Numerical Analysis 20 (2) (1983), pp. 345–357. DOI: 10.1137/0720023
  • Elman, H.C., 1986. A stability analysis of incomplete LU factorizations, Mathematics of Computation 47 (1986), pp. 191–217.
  • Gerhold, T., 1997. Calculation of complex three-dimensional configurations employing the DLR TAU-Code. Presented at AIAA Paper 97-0167.
  • Hall, K., and Crawley, E., 1989. Calculation of unsteady flows in turbomachinery using the linearized Euler equations, AIAA Journal 27 (6) (1989), pp. 777–787. DOI: 10.2514/3.10178
  • Hall, K., Thomas, J., and Clark, W., 2002. Computation of unsteady nonlinear flows in cascades using a harmonic balance technique, AIAA Journal 40 (5) (2002), pp. 879–886. DOI: 10.2514/3.15137
  • He, L., and Ning, W., 1998. Efficient approach for analysis of unsteady viscous flows in turbomachines, AIAA Journal 36 (11) (1998), pp. 2005–2012. DOI: 10.2514/2.328
  • Landon, R.H., 1982. AGARD R-702 compendium of unsteady aerodynamic measurements. Technical report. Neuilly sur Seine, France: Advisory Group for Aerospace Research and Development – NATO; 1982.
  • McMullen, M., Jameson, A., and Alonso, J., 2006. Demonstration of nonlinear frequency domain methods, AIAA Journal 44 (7) (2006), pp. 1428–1435. DOI: 10.2514/1.15127
  • Mialon, B., and Khrabrov, A., Khelil, S.B., Huebner, A., Da Ronch, A., Badcock, K.J., Cavagna, L., Eliasson, P., Zhang, M., Ricci, S., Jouhaud, J.-C., Rogé, G., Hitzel, S., and Lahuta, M., , 2011. Validation of numerical prediction of dynamic derivatives: the DLR-F12 and the transcruiser test cases, Progress in Aerospace Sciences 47 (8) (2011), pp. 674–694. DOI: 10.1016/j.paerosci.2011.08.010
  • Mortchelewicz, G., 1998. Application des équations d'Euler linéarisées à la prévision du flottement. Neuilly sur Seine, France: AGARD; 1998, Technical report AGARD R-822.
  • Murman, S., 2007. Reduced-frequency approach for calculating dynamic derivatives, AIAA Journal 45 (6) (2007), pp. 1161–1168. DOI: 10.2514/1.15758
  • Pueyo, A., and Zingg, D., 1997. Progress in Newton-Krylov methods for aerodynamic calculations. Presented at 35th AIAA Aerospace Sciences Meeting and Exhibit. 6–9, January, AIAA-97-0877.
  • Saad, Y., 1994. "Krylov subspace techniques, conjugate gradients, preconditioning and sparse matrix solvers". In: Von Karman Institute for Fluid Dynamics Lecture Series 1994–05. 1994, 21–25 March, Brussels.
  • Saad, Y., 2000. Iterative methods for sparse linear systems. Self Published. 2000.
  • Thomas, J., Dowell, E., and Hall, K., 2002. Nonlinear inviscid aerodynamic effects on transonic divergence, flutter, and limit-cycle oscillations, AIAA Journal 40 (4) (2002), pp. 638–646. DOI: 10.2514/2.1720
  • Thomas, J., Dowell, E., and Hall, K., 2004. Modeling viscous transonic limit-cycle oscillation behaviour using a harmonic balance approach, Journal of Aircraft 41 (6) (2004), pp. 1266–1274. DOI: 10.2514/1.9839
  • Timme, S., Marques, S., and Badcock, K.J., 2011. Transonic aeroelastic stability analysis using a Kriging-based Schur complement formulation, AIAA Journal 49 (6) (2011), pp. 1202–1213. DOI: 10.2514/1.J050975
  • Wong, P., and Zingg, D., 2005. Three-dimensional aerodynamic computations on unstructured grids using a Newton-Krylov approach. Presented at 17th AIAA Computational Fluid Dynamics Conference. 6–9, June, AIAA-05-5231.
  • Woodgate, M., and Badcock, K.J., 2009. Implicit harmonic balance solver for transonic flow with forced motions, AIAA Journal 47 (4) (2009), pp. 893–901. DOI: 10.2514/1.36311

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.