Hopf bifurcation calculations for a symmetric airfoil in transonic flow

AIAA Journal

Volumn 42, Issue 5, 2004, Pages 883-892

  Badcock, K J ^a,b   Woodgate, M A ^a,b   Richards, B E ^a,b  

^a UNIVERSITY OF GLASGOW   (United Kingdom)

^b Department of Aerospace Engineering ^*  (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

AIRFOILS; BIFURCATION (MATHEMATICS); COMPUTATIONAL FLUID DYNAMICS; COMPUTER SIMULATION; LINEAR SYSTEMS; MATRIX ALGEBRA; NONLINEAR EQUATIONS; RUNGE KUTTA METHODS;

COMPUTATIONAL STRUCTURAL DYNAMICS (CSD); EULER EQUATIONS; MACH NUMBER;

TRANSONIC FLOW;

EID: 2542489301     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/1.9584     Document Type: Article

References (22)

1. Goura, G. S. L., "Time Marching Analysis of Flutter Using Computational Fluid Dynamics," Ph.D. Dissertation, Dept. of Aerospace Engineering, Univ. of Glasgow, Glasgow, Scotland, U.K., Nov. 2001.
2. Lesoinne, M., and Farhat, C., "High Order Subiteration-Free Staggered Algorithm for Nonlinear Transient Aeroelastic Problems," AIAA Journal, Vol. 36, No. 9, 1998, pp. 1754-1757.
3. Djayapertapa, L., "A Computational Method for Coupled Aerodynamic-Structural Calculations in Unsteady Transonic Flow with Active Control Study," Ph.D. Dissertation, Dept. of Aerospace Engineering, Univ. of Bristol, Bristol, England, U.K., Nov. 2000.
4. Farhat, C., Geuzaine, P., and Brown. G., "Application of a Three-Field Nonlinear Fluid-Structure Formulation to the Prediction of the Aeroelastic Parameters of an F-16 Fighter," Computers and Fluids, Vol. 32, No. 1, 2003, pp. 3-29.
5. Melville, R, "Nonlinear Simulation of F-16 Aeroelastic Instability," AIAA Paper 2001-0570, Jan. 2001.
6. Silva, W. A., Beran, P. S., Cesnik, G. E. S., Guendel, R. E., Kurdila, A., Prazenica, R. J., Librescu, L., Marzocca, P., and Raveh, D., "Reduced Order Modelling: Cooperative Research and Development at the NASA Langley Research Center," Proceedings: International Forum for Aeroelasticity and Structural Dynamics, Vol. 2, Asociacion de Ingeneros Aeronauticos de Espania, Madrid, 2001, pp. 159-174.
7. Beran, P. S., and Carlson, C. D., "Domain-Decomposition Methods for Bifurcation Analysis," AIAA Paper 97-0518, 1997.
8. Morton, S. A., and Beran, P. S., "Hopf-Bifurcation Analysis of Airfoil Flutter at Transonic Speeds," Journal of Aircraft, Vol. 36, 1999, pp. 421-429.
9. Beran, P. S., "A Domain-Decomposition Method for Airfoil Flutter Analysis," AIAA Paper 98-0098, 1998.
10. Badcock, K. J., Richards, B. E., and Woodgate, M. A., "Elements of Computational Fluid Dynamics on Block Structured Grids Using Implicit Solvers," Progress in Aerospace Sciences, Vol. 36, 2000, pp. 351-392.
11. Osher, S., and Chakravarthy, S. R., "Upwind Schemes and Boundary Conditions with Applications to Euler Equations in General Coordinates," Journal of Computational Physics, Vol. 50, 1983, pp. 447-481.
12. Van Leer, B., "Towards the Ultimate Conservative Conservative Difference Scheme II: Monotonicity and Conservation Combined in a Second Order Scheme," Journal of Computational Physics, Vol. 14, 1974, pp. 361-374.
13. Cantariti, F., Dubuc, L., Gribben, B., Woodgate, M., Badcock, K., and Richards, B., "Approximate Jacobians for the Solution of the Euler and Navier-Stokes Equations," Aerospace Engineering Rept. 9704, Univ. of Glasgow, Glasgow, Scotland, U.K., March 1997.
14. Jameson, A., "Time Dependent Calculations Using Multigrid, with Applications to Unsteady Flows past Airfoils and Wings," AIAA Paper 91-1596, 1991.
15. Goura, G. S. L., Badcock, K. J., Woodgate, M. A., and Richards, B. E., "Implicit Method for the Time Marching Analysis of Flutter," Aeronautical Journal, Vol. 105, No. 1046, 2001, pp. 199-214.
16. Seydel, R., Practical Bifurcation Analysis and Stability Analysis, 2nd ed., Springer-Verlag, Berlin, 1994.
17. Cantariti, F., Dubuc, L., Gribben, B., Woodgate, M., Badcock, K. J., and Richards, B. E., "Approximate Jacobians for the Solution of the Euler and Navier-Stokes Equations," Glasgow Univ., Aerospace Engineering Rept. 5, Glasgow, Scotland, U.K., March 1997.
18. Bischof, C., Carle, A., Corliss, G., Griewank, A., and Hovland, P., "ADIFOR: Generating Derivative Codes from Fortran Programs," Scientific Programming, Vol. 1, IOS Press, Amsterdam, 1992, pp. 11-29.
19. Badcock, K. J., Xu, X., Dubuc, L., and Richards, B. E., "Preconditioners for High Speed Flows in Aerospace Engineering," Numerical Methods for Fluid Dynamics, Vol. 5, Oxford Univ. Press, Oxford, 1996, pp. 287-294.
20. Axelsson, O., Iterative Solution Methods, Cambridge Univ. Press, Cambridge, England, U.K., 1994.
21. Tuminaro, R. S., Heroux, M., Hutchinson, S. A., and Shahid, J. N., "Official Aztec User's Guide," Ver. 2.1, Sandia Lab., Rept. SAND99-8801J, Albuquerque, NM, 1999.
22. Burden, R. L., and Faires, J. D., Numerical Analysis, Prindle, Weber, and Schmidt, Boston, 1985, Chap. 8.